Well, I guess you could always upload a arbitrary wave with such a shape that it is effectively a square with 38ns risetime

Maybe one such wave for 1MHZ, one for 10MHz etc. After all, you got a shitload of 64 ARB positions. One for each of your desired risetimes.

What I did find is that if you take a square, and modulate it with PSK with another square of the same frequency, I get a nice 4.4ns risetime square wave!

I think that is really impressive. I was playing with time-domain reflections to measure length the other day. with a <5ns device I should retry that play.

Edit: In fact, all the vertical edge waveforms (pulse, cmos, reverse sawtooth, all of them), *except* the square seems to be 4.4ns. Only the square has 7.8ns.

And indeed, much cleaner to see cable reflections with 4.4ns. Now I know my pieces of BNC-coax are about 1mtr in length