“There seems to be more leg blood clots than expected” The clotting is caused by the body devoloping antibodies to the virus already nascent in the body(hence the warning about giving the drug with HPV already present) The antibobodies clump and stick onto the millions of virus in the body causing danger of clotting, especially when the vaccine is given...the body attacks the vaccine !
Do you have a reference? 90% of the Deep venous thrombosis cases have known risk factors. The jury is still out on whether there’s a true association, much less causation.
There’s no such warning about prior infection - only about allergy to yeast and/or to prior vaccinations for HPV.
http://www.gardasil.com/what-is-gardasil/information-on-gardasil/index.html#eight
The viruses don’t circulate in the blood the way you describe.