Don’t get confused by the second if not being a conditional at all, but rather the version that means whether. Try changing your second if to either that or to whether for a clearer read.
That just puts off the decision of what tense/mood to use. The issue there is that whether clauses could indeed historically trigger the subjunctive in the verb they governed, whether it be present or past, in and by themselves.
Nowadays you invariably get indicative in the present, but people still waver about the subjunctive when back-shifting it. Both variations occur in the wild, no matter whether they are “right” or “wrong” — whatever that means. (But not “no matter whether they be” — nobody says that anymore.)
- I don’t know whether she is/she’s ready.
- I didn’t know whether she was ready.
- I didn’t know whether she were ready.
Given that, “If I were he, I would doubt that she were serious” does not lack for historical support, but it is a bit stuffy — a little bit for some, too much for others.
“If it were me, I’d doubt she was serious” is how most people would say it today, except in super-stuffy writing. You could even get by with a simpler “Me, I’d doubt she was serious.”
For further reading with an historical perspective on all this and copious examples, I strongly recommend F. T. Visser’s monumental An Historical Syntax of the English Language, in two volumes, covers this simple matter in only around 250 pages of his second volume, treating with Old English, Middle English, Early Modern English, the stuff between then and now, and Contemporary — or as Visser calls it, Present Day English.
Here is a Google Books link to Visser’s second volume, to the portion covering “modally marked forms” (nées subjunctives) in various circumstances. Start reading a hundred pages or more earlier than that point, though, back when it first starts.
You do have to get used to his peculiar terminology of modally marked forms, but his scholarship and examples are, well, exemplary. It really is FMTEYEWTK on the subjunctive in English.