It's definitely an idea worth considering, though ...

It's definitely an idea worth considering, though I wonder whether your caveat about incentivising the firearms market could be avoided by making this a one-off, week-long exercise rather than a permanent scheme. In that way there simply wouldn't be time to organise the import or manufacture of further weapons for profit. Personally I would tweak the rewards to make it more tempting to provide intelligence than simply hand over the gun with no contextual information about who owned it, their associates etc.