Bottom heat is why your seedlings are getting so leggy. Ease off it asap and go ahead and prune the tops. You will get more bottom growth and make it a lot easier to transplant without tangling up the tops.

I just use heat for germinating, then actually move the seedlings into a very cold, bright window and they do just fine w/o heat here in zone 6. I still have to trim onion tops on those started early, tho the plants are not weakly leggy. It's because they tangle in a flat and flop some anyway. Probably not needed, but easier for me to bottom water individual containers as needed.