回复：H1》F2》H1?

To my acknowlege, it is practical to go with a pathway as you said. However, The time frame of H1 to F2 might take longer time, saying 9 months, and while you are waiting for F2,You are unable to apply H1 even you find a job, otherwise, you must take a risk to go 3rd country for H1 visa and give up your pending F2.
Lily