I can't speak to the heat that you personally will encounter, but in any case May 12th doesn't sound all that late to me. ADZPCTKO is late April; I started in late April my year (right after the KO) and was dead in the middle of the herd.
If you're a particularly slow hiker, then you might have less interaction with folks, but you'll still see people. I live in WA state and the tail end of the herd came through pretty late --- I did an early October backpacking trip between Snoqualmie and Steven's passes and ran into a surprising number of thru's still at it.
Your specific points:
1) won't be starting too late for a dangerous heat while in the desert
I doubt it, but every year is different. Worse comes to worse, do some (or a lot) of night hiking, take a mid-day siesta. You do have Yogi's guide, don't you? If not, buy it pronto and read it. Then process what you read and then read it all again.
2) I won't be too far behind the pack in the sierra and will be hiking without company
Depending on hiking speed I think you'll find company. I got off trail for a week at the OR/WA border, and hiked all of a day or two before connecting up with a fellow who I hiked with to Stehekin (for example). I would lose connection with people on the trail and then sometimes run into them again. The trail is like a river and thru's are the flotsam and jetsam floating around in different eddies.
Particularly this year, it's suspected that more folks will be out there due to the latest popular book on the theme of "I hiked just part of a major trail and wrote a lot of hype about how grossly unprepared I was and what happened as a result of my stupidity" (the Oprah-blessed book 'Wild'). This certainly happened on the AT after Bryson's book made it big; TBD how much effect this might have out west, but likely some.
3) Won't be hiking on really hard compact snow pack where an ice axe will be needed
Check the snowpack data (postholer.com has this), see how it's shaping up vs. a typical year. In any normal year you will encounter snow. Very much depending on snowpack as well as on how fast you hike the first 700 - 800 miles you might or might not want an ice axe. It's wildly unlikely that you won't run into SOME snow. And creek crossing issues as well.
Overall a May 12th start date doesn't sound bad to me, so long as your pack isn't too heavy and you do some modest prep. Your AT experience should surely help you on those things.