yes, the XT/XTK (in fact all microwaves) will let you load up your own waves. the waves are 64 samples long, 8 bit waves, single cycle, and you send them over via sysex, then a wavetable (which is 61 waves long, and is basically 'you put wave X in slot 0, you put wave Y in slot 1, etc'. there are some programs that can help with this (including sound diver). so you can make your own waveforms and use them, or a whole wavetable and scan across them.
on the asr-x, remember i don't have an ASR so this is all from research.
first thing you have to do is get ASR-X Tools, afaik (or find the sysex spec, the program is like $39 i think. you can also buy a transwave CD out there for like $39 too). basically, in the 'loop mode', there's like forward, backward, forward + backwards, whatever. internally there's another option 'transwave', but you can't access it from the front panel - ASRX tools uses sysex to turn it on.
a transwave is 'just another sample' in a special format... iirc, each wave in the sample is 128 samples long, single cycle, and it can access up to 128 of them.
there are some programs that assist you with making the transwave samples (including asr-x tools, and a couple freeware things i've found). the first 128 samples in the waveform is wave 0, the next 128 samples in the waveform is wave 1, etc. all the way up. to get it to work properly, you need to make sure they begin and end on zero crossings etc. or it might click when you change waves.
i guess you can program using the existing transwaves too, but like i said i've never used one.
the old ASRs use the transwaves exactly the same, except AFAIK you can just choose the transwave loop mode from the front panel. the ASRX obviously doesn't support it as well as the 'old' ASRs from the front panel, but it has the whole MR synth engine in it (including a pair of resonant filters per voice), whereas the old ASR only has non-resonant filters (or a resonant filter in the effects section).
i keep mentioning the MR rack w/flash, you can't find the MR-flash anymore though. it would allow you load in up to 8M of samples, and i think they can be transwaves. i am thinking this would be the best of both worlds (front panel that supports transwaves and everything else, with the filters too), but i haven't actually tried it. and i already have an XT