I like the idea of a hole in the end of the ram. I have a ratcheting 5 ton hand press in my shop, but I think a 1/2 ton or 1 ton would do better.
With a tight tolerance ram and something like a pin vise with close fit into such a hole would allow the pin to be started using the pin vise jaws to hold the pin from tipping sideways for the first fraction of the insertion, then once it's started the pin vise could be taken out and the end of the ram used to send it home.
My experience with pushing long thin rods into holes without any means to keep the pin vertical is that most arbor presses have enough slop that the slightest bit of non-alignment will cause the arbor ram to move sideways far enough to exacerbate the difficulty, and add to that a receiving frame not secured against sideways movement and you have a good method for scratching up a gun.
Videos I've seen of guns being assembled by the makers have shown them tapping the pins in with a hammer, though I'm not trying to imply that presses aren't used by some.
A hammer and solid foundation under the gun, plus experienced hands, works very well indeed. I've driven many pins in Sigs that are true interference fits using a small ball peen. My experience with the Sigs is that getting them out is much more difficult than getting them back in.