Trade value, private sale value and trade-in value are going to be wildly different.
Trade value - you're trading your Papoose for a different gun with someone - will be the highest, but their trade value will be elevated too. This will be the value in line with unsold guns on gunbroker or asking prices on armslist.
Private sale - probably in line with completed sales on gunbroker for a similar setup as FOUR4D4 pointed out.
Trade-in - what a dealer will give you for a trade-in value towards a new gun from their stock, this will be the lowest, bordering on insulting.
It may be a little time consuming but you can download the old Amoskeag Auction silent auction catalogs as pdf files, do a CTRL-F search for "Papoose" and then look up the sold for prices in the spread sheet they post. One minor point, the sold for prices will not include the 15% buyers premium so, the winning bidders actually pay what's listed plus 15% for the gun.