That's not how supply and demand works.
If there are less stolen guns coming into the black market, then the general price of black market guns rises. Individual transactions do not have a price set in stone, because there is competition. e.g. if you taxes every gun except the AR-15, then the price of all other guns would rise, but so would AR-15s because now there's more competition to buy that particular gun (and less demand for the other guns). You don't have to apply "tangible" costs onto the price of the AR-15 directly, the price of other guns going up causes the AR-15 price to rise by itself.
for smuggling, I'd argue that the smuggling only makes up the tiniest proportion of the guns used in crime. So it's a red herring to say you can keep open gun availability but cracking down on "smugglers" would solve the issue. It's a false deflection. In fact, the whole border issue was that Mexican gangs buy guns in America then they smuggle them south to use in the drug wars. It's not them, it's you. It's a complete red herring that you're being awash in foreign guns and that border protection would solve it. You guys are the prime source of the guns. It's fucking nuts to hold up border security as the solution here.
And like I said, the criminal wanting to use a gun illegally is constrained by the cost of the gun. If the price of black market guns rises, then the profits of gun crime are reduced, which pushes more marginal uses into the "not profitable" category.
Sure, that might not stop a really determined mass-shooter, but almost all gun homicides are not by mass-shooters, they're by petty criminals discharging the gun in pursuit of some frankly not very profitable venture. If you push the cost/profit line south for that, then less of them are in the market for guns.