I can't see from this angle how far the spigots protrude up, but they need to go all the way into the head recesses in order to work right. And that means they have to go all the way up in there with the gaskets in place. If that is not happening, then there will be problems until that is corrected.
You can cut the barrel gasket mating surfaces on a lathe, without cutting the spigots, until you have removed enough material to have taller spigots. Measure as you do it, and make it so there will be enough spigot to fit full-depth into the head recesses with the gasket in place and crushed.
Alternatively, you can cut off the spigots entirely, but then you will definitely need a new head gasket type that has a fire ring, or is a solid copper type gasket. Then there are no concerns about spigot height anymore, and the gasket thickness just needs to be taken into account as to how high it sets the heads off the barrels, because that gasket thickness will affect the compression ratio. Like a car.
And if the head recesses overhang past the edge of the head gasket, they should be welded-up or filled with something that can't burn out, because any overhang of the empty spigot recess over the edge of the head gasket can cause the head gasket to blow.
You can do it either way. But it needs to be done right, whichever way you pick.