The block is curved, so applied by rolling horizontally. Problem is it's unbalanced - almost everything is on the top of the block, so makes it hard to apply in a level manner.
Good tip ono the "something soft underneath". Putting some craft foam underneath the paper helped quite a bit - doing it that way, I'd say I was getting 1 perfect one out of every four, and maybe another 2 of 4 weren't perfect, but usable. So I'm still thinking breaking it up into two or three smaller stamps is the way to go.
On another front, I picked up some Foma 3.25" x 5.5" paper and gave that a go. Took this as an opportunity to redo the text also, which now I think may be too small (I swear, I calculated this all out.... oh well). Didn't notice the text had smudged until now... I'll have to look and see if that's an issue with the transparency I printed the text on or some kind of goober on the glass/negative. As the paper is the exact size of the negative, gonna be hard to not get a hair of burn somewhere around the edge. I think that's ok though, and the kind of impreciseness that helps with the nostalgia.