If you can't find a dealer to handle this properly for you, and assuming your uncle can disassemble it, and you know how to reassemble it, I would have him take it apart and package **each part** separately in its own box (using appropriate packaging). If each part is boxed separately it's less of an issue what type of padding is used, so bubble wrap and (yes, even) peanuts will be good for your purpose. Packing/shipping parts will be safer and probably cost you less than asking a dealer to pack it for you.
So for example, remove the Tonearm (remove the cartridge first). This is the most fragile part . . . make sure it's securely wrapped up and there's good cushion in an strong box. Similarly, pack the dust cover separately - need a strong box for it. Remove the platter . . . etc. Once you get it down to the plinth/chassis you have the heaviest part. Some of these individual boxes may fit together safely inside another box, but I wouldn't go overboard trying - you won't save that much money. All of the boxes/material you need can be bought at UHaul or Staples, etc.
This is perhaps more bulletproof than you need but I've had 2 TT's packed by dealers and shipped to me and BOTH arrived damaged because they tried to put everything in one box. And for god sake, do NOT let the UPS store package it for you. It's just as good as asking them to hold on to your cash (whatever you paid for the TT) for the 3 months it will take until they honor the insurance claim.
Here's a link that also shows some principles for packing TT and may help:
TT Packing