Dave, The wheels used in this mod are 14" tall. They work great and I highly recommend this mod. As for the leg end of your Platinum, I would measure the OD of them and see if I could get some pipe that has the same ID. Cut them to your required length and slip onto the legs. Secure them with SS screws or bolts and you should be good to go. If your planning on putting caps on the leg extensions, don't forget to take into account the extra hight. When you do this, don't forget to share your progress with the rest of us.
On the note of the legs becoming loose and falling out of Kettles, I just give the legs a little squeeze with Channel Locks and shove them back in. I've had on occasion, had add some Aluminum Foil as a shim to tighten them up. (Didn't have any pliers handy at the time.)