I think the buybacks are great. It gets guns out of the hands of those too stupid to know what their rights are. A government supported version of Darwinism, if I may.
Just think, if they'll trade their guns for what is normally a free inoculation and a few dollars, would you want them watching your back during a civil war?
A friend from years back told me this would justify buying old junk guns. Pick up a dozen piece of crap guns and when a buy back hits you could make a tidy profit.
The problem with your proposition is that it establishes, in the mind of the general public, that the buy-back is actually getting the right guns off the streets. I'll give you a not-so-crisp FRN if you can provide documentation of a criminal turning in an illegally possessed firearm at one of these events.
An additional problem caused by buy-back programs is that they interfere with commerce, and often cheat the person turning in the firearm. If Granny no longer wants her late husband's Postal Meter M-1 carbine laying around in the back of the closet, that's just fine with me. But to exchange it for a gift card (usually under $100) and then destroy it causes the state/locality to lose tax money that would have been realized from the "controlled" sale at a price based on value as a collector's piece.
If you cannot/will not set up a spot on the sidewalk where you offer to buy for cash the guns being brough for turn-in then at least consider setting up with a copy of the Blue Book of Gun Values and helping the folks discover the worth of what they are bringing to be destroyed. f it's legal, set up a deal with your favorite FFL for a commission on every gun you send to them - that way Grammy, you and the FFL all make money from the deal, and of course you will all be paying the appropriate taxes which helps the locality's budget. Win/Win/Win/Win.
stay safe.