Once I put the heading tags back in my rankings dropped again.
How long did the page stayed on in the horrible new format before you put back headings/strong? What about changing one page back to horrible red and leaving it for 2-3 months to see if rankings hold?
It could be that by removing headings/strong, the page was sufficiently changed that resulted in some signals being reset so the page had to be re-evaluated again. It is also possible that some signals are folded in later on with the time (e.g. usage? maybe even inbound links?) which impact ranking later on.
Here is why I am saying this:
Few years back I had a page that Google kept getting the language wrong. This was a multilingual site, hosted in a country in Europe (not UK/Ireland), but with the home page in English. Suddenly out of blue Google declared the page language to be of the country it was hosted in and home page got "Translate this page" in SERPs. Ranking dropped a few places and CTR dived.
After a while I realised that every time I changed something more significant on the page (e.g. page title or more significant things in page structure), Google "fixed" the language and recognised it to be in English.... for the next 8 weeks. Then suddenly it said it was in foreign language again. I would change the title by swapping 2 words around, do a fetch and "Translate this page" would disappear... again for the next 6-8 weeks. So such changes were my work-around.
This had been going on for a year and was incredibly frustrating. I discussed this with Tedster whose theory was that when something significant on the page changes, it needs to be evaluated again. But this evaluation cannot use signals that would build over the time.. until some time passed.
I am wondering whether the similar thing could be here - that by removing headings and strong you have so much changed page structure that initially ranks well but could drop later on if the ranking is influenced by signals that build over time.