I would cut the HT at the top, after confirming that the tube ID will be in the ballpark after cutting, to where it only needs a little reaming (as is usually the case). No qualms about that at all. I used to make lugless bikes with thin 1-1/4" head tube, brazed on ring at the bottom, no ring at the top. No one ever had a problem with the top of the HT wallowing out or cracking.
I suppose if the HT is thinwall and low-strength tubing, you may have a problem, but even then I doubt it. But my frames with no ring at the top were always 531, Cyclex, or domestic generic 4130 "aircraft tubing". I never tried it with Hi-Ten or lower quality tube. Do we know what your frame is made from?
Do you know someone who can ream and face the HT after you cut it? LBS, local framebuilder or extreme nutcase like me who just happens to have a HT reamer?
I didn't see any mention of where you are — I always encourage people asking questions like this to include their city/state so we can point you to someone local to you.
Mark B in Seattle