I've tailored my code to validate in both HTML and CSS, to have acceptable semantics, and to be mobile-ready.
In addition to the problems I've had controlling page rendering, it's my impression that these can affect pagerank. Is there an acceptable way to bypass server-inserted code? (Is it, simply, a matter of finding a different host?) I would surely appreciate your advice.
You need to find a different host IMO or upgrade your hosting. The only experience I've had with hosts injecting code like that is on cheapo/free services where they will inject ads in the page. Difficult to remove (you can't remove it completely) and would probably break T&Cs.
A framed site gives the impression you are using "free" hosting that comes as part of an ISP contract. You can view the source if you view the "frames" source.