I've often wondered if you might want to put a "price good thru" caveat to the prices you quote? That way, it gives the shopper a time limit, which after expiration is not guaranteed. Might motivate a fence-sitter to "pull the trigger" knowing the price will likely change in 5 days, 7 days, or whatever is reasonable. Only you will know if that price is guaranteed for a any number of days.
Also, the "name your price" might be a good way to go, but it's almost like a "price match" option. If someone finds it online or sale priced on island, they should know they can bring that price to you to match or beat. Sometimes I get a good price online. If I know it's less than the shop has it priced, including shipping and FFL fee, I go ahead and order it before they sell out. Without a "price match" policy, I'm probably not giving you a chance to compete.
The main thing is to know whether you are willing to look into matching another vendor's price. Whether or not you can match the price, at least it gives you the opportunity to try. Online processing of these requests is necessary, as some sales might be short-notice and subject to expiring or selling out very quickly.
Just a few thoughts for your consideration.