A friend of mine once had some of his favorite speakers redone in the same way, for exactly the same reason. He hired a professional to do the work, but I'm curious about the process, wondering if it was difficult to do yourself?
That's how I first heard about it too -- a buddy paid to have some woofers "professionally refoamed."
It turns out the process is very easy, requiring only the new foams, a snap-blade knife, some Aleene's® Original Tacky Glue®, Isopropyl alcohol for helping soften/clean the old glue residue, clothespins for clamps (optional), and about two hours (for me anyway) to do a pair of woofers. There are lots of youtube videos showing the entire process, almost in real-time, at perhaps 15-25 minutes per woofer.
Two basic approaches seem to exist: with and without shims. If you go the shim route, it takes about twice as long to do. I didn't bother with the shims, and am very happy to have avoided all of that extra/unnecessary fuss.
With really large woofers, say 12" or more, the shim method might add value, as the larger diameters are trickier to keep centered on the voice coil without shimming. But for the 6" and 8" ones I did here, there was no fuss at all in keeping them centered.