If the grease has dried out then you can certainly get some strange squeaky noises - mine was at the stage that the grease looked more like clay. It's quite easy to have the joint cleaned and lubricated - I usually drop the rear exhaust mounts and take out the whole driveshaft. There's a pressed steel cap over the joint which just taps off when it's out of the car.
A replacement CV should only be needed if the joint has been loaded dry unlubricated for quite some time...they're made of pretty hard stuff.
The easiest thing to do would be to remove the shaft to the rear axle completely - should be a 30 minute job. Then take it for a drive for a while. (It will drive perfectly fine in front drive only without any errors... If the problem is "solved", then take a look at the CV joint. It wouldn't hurt to clean and lube it whilst it's out either way though...)
My logic is that with your new mounts, the engine won't be moving as much as it was, therefore the CV joint won't be flexing as much and the sound has "improved" as a result. Good luck.