If you move, you are correct that you would be "worse off" (financially) than you are now, but the things you are comparing are actually independent from each other. Consider these hypotheticals:
- You currently live in your parents house and pay no rent. If you choose to rent an apartment on your own, you would be "worse off".
- You currently live in a paid off home with total monthly expenses of $1000/month. You rent out the home for $2000/month (profit $1000/month and say after taxes you keep $650/month), and go rent a house. If the house you rent is less than $1650/month, you are "better off" and if it is more than $1650/month you are "worse off".
The idea here is that you are trying to compare (the large advantage of) living in a paid off home to renting another apartment, and these two things shouldn't be compared in that way, because, of course you're better off living in a paid off home, just like you would better off living with a friend or relative and paying no rent.
It may help to reverse the thought experiment: Suppose you are renting an apartment, and you suddenly acquire a paid off home (perhaps through inheritance). You may choose to rent out the home, presumably make a profit, pay some taxes, and be "better off" than when you didn't have the home. Or if the location is convenient, you could move into that home and be "even better off" since you'd likely save more in rent than you profit from renting out the house. So to answer your specific question of
What is the most financially efficient way to change one's
residence?
the answer may simply be:
To move into a friend or relative's house, or one that you already
own outright.
The fact that your home is paid off is making it seem like you're worse off if you move, but it probably wouldn't feel that way if you still had a mortgage.
Old answer due to different wording of the question about deducting "rental expenses":
In Canada, like in the US, you can deduct rental property expenses. This doesn't apply to you, but note that if you were to have a mortgage, you can only deduct the interest you pay, not the principal, so it could be the case that your cash flow is negative but you still profit overall when you add in the equity you're gaining each month.
One significant difference between the US and Canada tax law is that in the US rental property depreciation is mandatory, whereas in Canada the equivalent concept, called Capital Cost Allowance (CCA), is optional. In your stated scenario where the expenses equal the income, I'm guessing you'd be better off not taking CCA because it would cause a loss, and it may be better to save the deduction for when you have a gain or when you sell the property.