h1b and EB category are completely separate process. You can apply and should definitely apply both. TPS should be able to cover you up for your EB process but its temporary and no one knows if this will be renewed(factually) but it does hold a strong ground for renewal. My personal advice, apply for H1b but start for the EB process ASAP.
You will have your GC in next 2 yrs at the latest.
And don't forget to invite me to the party.