"I think that the state could apply to the Federal Government to convert a federally funded freeway to a tollway..."
Presently true. In the next Transportation Bill (likely to pass earlier this year) they won't even have to apply. A rogue governor, for example, can simply decree that his Interstates will be Toll Roads. But that would never happen in Texas (ha).
Shouldn't there be legislative approval for such a conversion? after all, it could come under raising revenue, and the people should be involved in such a thing.