I have built an underhammer on the Blue Grouse variant of the H&A action. While it is certainly a reliable and capable rifle, I cannot recommend that style of action for several reasons. For one, they are darn heavy for what they are. For another, the set up of the rear of the breech and the through bolt that attaches the buttstock makes for rather limited geometry options and requires lots more drop than I like. Thus, recoil is more significant than it needs to be. I am not a huge fan of the mainspring trigger guard either.
Finally, it was difficult, in my case, to keep the nipple ahead of the breech plug and yet reachable for the hammer. This may have been due to the way my Blue Grouse action mounts the barrel (screwed, not pinned), but be ware that you want your nipple not only in front of your breech plug but in front if it with a bit of a margin to spare - maybe 1/10" or so, if possible.
Trigger options the H&A are pretty limited, but you can make a decent single, nonset trigger with a bit of tuning.
Overall, I think there are many other underhammer styles I would prefer. The Billinghurst style is better in my opinion, but there are others as well. I cannot comment on the Pete Allen version.