This is a really good question. Here are a few suggestions, perhaps just pick one or try a couple. This advice comes from my experiences as a player and a GM.
Engage the New Players as much as you can
Babysitting is not my idea of a fun RP session, so I get where you are coming from, but perhaps there is a way to enliven the game by challenging the new players a little through engagement from you and your experienced team.
Lead by Example: Continue playing the way you have always played, as much as possible, but be open to the new players and their suggestions.
Give them space: It might be hard to look around the table and wait for the rogue to realize he's the one who has to check for traps...but give them space to come to this on their own.
Spotlight: Find a reason to throw one of the new players into the spotlight. Ask them for help or to use their character's abilities (can they open the door? turn undead? would they mind strapping light steel shields all over themselves and running through a goblin-infested square as a diversion for you, pretty please?). Basically, ou are asking the other player to engage in a meaningful way to the game-play and also role play...kind of demonstrating the whole thing but through their own actions.
Constructive, OOC Feedback: Try not to show that you feel you are babysitting at the table, but I think it's important to let the new players know what they are doing really well, and what they need to work on. Ask about their characters and how their character feels about the setting/situation/actions. Wouldn't their character (a druid) care about this thing (the wizard haphazardly burning down the forest) and want to act/engage? This gets new players thinking about what their character should be doing and how they could act.
Talk to the GM
Re-introduce Rules: There may be age-old rules and table courtesies that the GM has forgotten to let the new players in on because you guys just know them. Things like:
- Work out your character's action before their round.
- Know your spells/special abilities/feats/equipment (make notes!) before play so that you aren't looking up the rules as you go and taking up game time.
Character Background: You guys probably have a standard level of character background needed because you've been playing together, comfortably, for years--but the new players don't have that advantage. Perhaps the GM, maybe with your help, needs to encourage the new players to build up some character background and knowledge.
Side Adventure: Let the GM know how you are feeling and ask them if they'd be willing to run the occasional side adventure for your usual gang so that you could go back to your preferred style of play every now and then. It should be a different campaign and set of characters, something to sate your desire for comfortable, fast, immersive play while the new players catch up and learn.
Split the Party?: Normally, inadvisable (as you probably know), but perhaps it could be useful for a session. In my experience it has been useful to split up a large party in specific circumstances--perhaps there is a time constraint and more than one objective, making it feel necessary for the group to split up (play each group on their own initiative or host a session for one group, and another session for the other).
Splitting and mixing new players with old players is useful because everyone in the smaller groups becomes that much more useful--and more keenly aware what they miss from the larger group (i.e. a helpful flanker, an AoE spellcaster, a buffer). After this experience the new players might come to respect the aspects of each of the other classes a little bit more and perhaps see other ways around obstacles besides hack-and-slash.
That said, this last is more circumstantial. If it is built in by the GM, it may seem contrived or a little deus ex machina. It also means more quiet time for players at the table in the group not active and/or half of the party missing one week at a time until the party reunites. Talking with the GM about it might be the best way to execute this particular suggestion.
