It’s an interesting hypothetical: Where someone who is clearly ineligible to be President or VP due to having served two prior terms as President, is serving as Speaker when the current Pres and VP become incapacitated, is that Speaker eligible “in the breach”?
I agree with your guess that this Speaker would probably serve as Acting President for a short time, but given the clear intent of the 22d and (last sentence of) the 12th Amendments, his/her continued service may lead to a constitutional crisis. Ideally, such a Speaker-turned-Acting-President would offer to step down (and return to the Speakership) in favor of the Senate President pro tempore, Sec. State and so on.
I read something not long ago about why having the Speaker of the House as next in line after the Vice President is a bad idea for several reasons. It's up to Congress to set the order of succession and it would be better to go back to having the Secretary of State next after the VP (well, in general, maybe not right now given the trail of convenient mysterious deaths which followed in the Clintons' wake).
I suppose a Speaker who became Acting President could nominate a Vice President, and then resign after the VP was confirmed--but the Speaker would then have no job to go back to.