Newbie here, some questions about functions and usability.

[xandorz]

The main issue with what you are asking if it is possible is that you say that there will be a lot of target swapping.

Without focus you can't really control from tank and use CC on a different mob than you are targetting from the tank.

You could control from 1 mage and use mouseover polymorph on it. Then you could also set it up so other mage has a macro to assist mage 1 and polymorph that target, allowing you to polymorph 2 targets without any swapping of windows.
So this would require you to control from a mage and use IWT on the warrior to run to mobs (might not play too good, but only way I can think of doing that).

Another way that might be possible to use 1 CC is to use healer as a "focus". If healer doesn't need to target anything else it could target the mob that needs to be CCed, and then the mage assist the healer before using Polymorph.

Another way you can handle the CC is by target mob 4 with tank. Press a button to assist on Mage 1. Target Mob 5 with tank. Press a button to assist on Mage 2. Target Mob 1. Pull mob and hit Polymorph button. No swapping window and 2 mobs are CCed.
To CC mob 5 again you can either target it with warrior and tell Mage 2 to polymorph it again. Or have the healer also assist when you did the pre-pull targetting and make Mage 2 assist the healer when re-polymorphing.

Healing you can do with mouse healing (it is some videos on how to send mouse clicks to the healer(s) when controlling another character).
You can do the same thing with dispelling, I would use Vuhdo (I mainly like how you setup debuff tracking for pvp so you can specify exactly what debuffs to look for so you see the second someone hit a CC you press it and dispel it).
I think you can make a different area of the hp bars send spells to different character, so if you right click on the left of the hp bar it tells mage to remove a curse from that target. If you right click on the right side of the hp bar it tells priest to dispel a magic. If you left click it cast a heal... Things like that.

There is people that have done many things, 40 box MC (when it was possible to automatically heal and dispel with addons, won't work in classic but for 5 man it is not needed), some have done 2200 rating in 5v5 arena. Some have done mythic dungeons in retail.

It shouldn't be any problem to multibox classic dungeons.