Let me get this straight.

You have existing 3 foot whips and you need 4 foot so you want to extend the existing whips 1 foot using a liquidtite coupling?

I have not seen or heard of such a thing.
The only option I am aware of is to use two connectors with a rigid coupling.

Have seen and used steel flex couplings but nothing for liquidtite.

As for tar build up, that can be a problem.

My suggestion would be to build a rack to mount the disco close enough so that they old liquidtite will get to it. Then run another piece of liquidtite to the unit. Yeah I know the boss will throw a fit because its obvious that he did not figure this cost into the bid.

By the way I agree with iwire, do you want us charging and recovering freon?