To pad out the difference between monergism and sunergism, let me quote from a different book:

"At the cross righteousness of God, justifying righteousness, was brought in by Jesus Christ. Not some vague, general, universal and inapplicable righteousness, potential to ‘all’ but effectual to none. But a specific, intended, particular and applicable righteousness, effectual to ‘all them that believe’. When justifying righteousness was wrought in death, then it was ‘unto’ them. It was not that they had received it: it was not ‘upon’ them. But it was wrought on their behalf: it was ‘unto’ them.

At the cross, by the faith of Jesus Christ, God wrought righteousness to the account of all his people. Then, it was ‘unto’ them. When in process of time they were brought to believe the gospel, that righteousness which had been wrought for them, which was unto them, was revealed to their faith in the gospel. They believed God, and it was accounted to them for righteousness. Then, that righteousness was ‘upon’ them. That is, ‘Unto all and upon all them that believe.’ [See Romans 3:21-25.]

Their believing answered to a work that was already effectual. It was already effectual when Christ died. The ighteousness was unto them. In particular. When they believed, that same ighteousness was upon them. Their believing added nothing whatsoever to the righteousness: it was the response of faith to the revelation of what God had wrought for them, and put upon them, in particular.

When Christ died, righteousness was brought in, and justification was effected, for all that believe. That is why Paul calls it henos dikaiomatos – ‘one accomplished righteousness’, Romans 5:18… In the Bible there is no question of a conditional atonement, or of a righteousness that must be qualified to become effectual.

Having absorbed all God’s righteousness in judgment on their behalf, in death all God’s righteousness rested upon him in peace and equanimity on their behalf… This is called, Being justified by grace. There remained, however, the imputing of this same righteousness, pertaining, as it does, to the experience of the believer. This, in turn, is named, Being justified by faith. The one is unto, the other upon, all them that believe… Here appears the folly of those who rob God of his justifying truth by saying, justification is a general work for all the world… [If so] then [God’s] work can only be completed if the good will of man concludes it by particularly accepting what he has generally offered. Equally, that work must remain ineffectual, and his love unrequited, if the ill will of man refuses to fulfil all righteousness by receiving it. All depends on man… assisting the Almighty to make it all possible. If this is not salvation by works, and the righteous being called rather than sinners, what it?

Hence Christ ought to cry ‘It is finished’ only when the essential condition of man’s acceptance is added to God’s general work in order to make it complete" [according to synergists]. Justification by Faith, John Metcalfe, pp 195-196 & 199-200, 1987 http://www.johnmetcalfepublishingtrust.co.uk/contact_us.htm

Both sets of quotes serve to show that the word 'choice' does not enter into monergism, while synergism depends on it. Until this crucial difference is understood, there will be no meeting of minds with the two 'camps'. But that is, essentially, why there is no dilemma to escape from, for the monergist.

To pad out the difference between monergism and synergism, let me quote from a different book:

"At the cross righteousness of God, justifying righteousness, was brought in by Jesus Christ. Not some vague, general, universal and inapplicable righteousness, potential to ‘all’ but effectual to none. But a specific, intended, particular and applicable righteousness, effectual to ‘all them that believe’. When justifying righteousness was wrought in death, then it was ‘unto’ them. It was not that they had received it: it was not ‘upon’ them. But it was wrought on their behalf: it was ‘unto’ them.

At the cross, by the faith of Jesus Christ, God wrought righteousness to the account of all his people. Then, it was ‘unto’ them. When in process of time they were brought to believe the gospel, that righteousness which had been wrought for them, which was unto them, was revealed to their faith in the gospel. They believed God, and it was accounted to them for righteousness. Then, that righteousness was ‘upon’ them. That is, ‘Unto all and upon all them that believe.’ [See Romans 3:21-25.]

Their believing answered to a work that was already effectual. It was already effectual when Christ died. The righteousness was unto them. In particular. When they believed, that same righteousness was upon them. Their believing added nothing whatsoever to the righteousness: it was the response of faith to the revelation of what God had wrought for them, and put upon them, in particular.

When Christ died, righteousness was brought in, and justification was effected, for all that believe. That is why Paul calls it henos dikaiomatos – ‘one accomplished righteousness’, Romans 5:18… In the Bible there is no question of a conditional atonement, or of a righteousness that must be qualified to become effectual.

Having absorbed all God’s righteousness in judgment on their behalf, in death all God’s righteousness rested upon him in peace and equanimity on their behalf… This is called, Being justified by grace. There remained, however, the imputing of this same righteousness, pertaining, as it does, to the experience of the believer. This, in turn, is named, Being justified by faith. The one is unto, the other upon, all them that believe… Here appears the folly of those who rob God of his justifying truth by saying, justification is a general work for all the world… [If so] then [God’s] work can only be completed if the good will of man concludes it by particularly accepting what he has generally offered. Equally, that work must remain ineffectual, and his love unrequited, if the ill will of man refuses to fulfil all righteousness by receiving it. All depends on man… assisting the Almighty to make it all possible. If this is not salvation by works, and the righteous being called rather than sinners, what it?

Hence Christ ought to cry ‘It is finished’ only when the essential condition of man’s acceptance is added to God’s general work in order to make it complete" [according to synergists]. Justification by Faith, John Metcalfe, pp 195-196 & 199-200, 1987 http://www.johnmetcalfepublishingtrust.co.uk/contact_us.htm

Both sets of quotes serve to show that the word 'choice' does not enter into monergism, while synergism depends on it. Until this crucial difference is understood, there will be no meeting of minds with the two 'camps'. But that is, essentially, why there is no dilemma to escape from, for the monergist.

SUMMARY - The straight answer is that no monergist can deny irresitible grace. The apparent dilemma asked about relates to non-monergists having a different view of 'choice' and 'making a decision' (either 'for' Christ or 'against' Christ) to that held by the monergist. Of course monergists have to weight matters of belief up and decide certain things! The crucial point, however, is subtle. It's shown in Romans 3:22, but modern translations have subtly changed that verse. Here's how it reads (the sentence starting in verse 21):

"And now apart from law hath the righteousness of God been manifested, testified to by the law and the prophets, and the righteousness of God [is] through the faith of Jesus Christ to all, and upon all those believing" Romans 3:21-22 Y.L.T.

Synergists think it is their faith in Christ that saves them.

Monergists realise that it was the faith of Christ, at the cross, that secured salvation to all who believe.

They believe the scripture that says Christians, who God foreknew, have been called by God, for he predestined them to be conformed to the image of the Son. God called them to faith, and - having called them - will he not give them that faith of Christ that secures salvation? (Romans 8:28-30)