I don't have an H, but I've used four boost pedals with my HXDA and DG30. These amps are pretty unlike one another, however the pedals I've gotten have been consistent with both amps, so there's that.
My favorite so far for most things is the clean boost that is part of the Fulltone Fulldrive 3. It has a really nice sound that brings out a little bit of the sparkle in the pickups, yet it doesn't fundamentally change the guitar's tone too much. It also has a built in limiter that you can dial in - or not - however the limiter is a germanium transistor based thing, and it sounds very good indeed, so I use it. That's my #1.
#2 is using the Fulltone Catalyst as a clean boost. This is the craziest damned pedal in a good way, because you can switch into being a fuzz, but as a clean boost it adds quite a bit of sparkle and a nice edge to the tone, and also works to make split humbucker pickups sound more like single coils. Obviously setup is crucial, and equally obviously, you have to control it with your guitar's volume knob, but I dig it and I don't even set it up for anything but clean boost these days.
#3 for me is the Xotic SP compressor, set up as a clean boost, with very slight parallel compression dialed in, and the blend knob set to mostly unaffected. In fact, this sounds an awful lot like the clean boost section of the Fulltone FD3, so I only use one of them, namely, the Fulldrive because I don't like having two things on the board that pretty much do the same thing.
#4 is the tried and true Fulltone Fat Boost.
Also tested: the Xotic EP Boost, but didn't like it very much with my gear. It seemed to conflict with the basic tones of the HXDA in an unpleasant way. Might be very good with a different amp, however, and it was certainly a quality piece in terms of build and so on.