As long as it hasn't ripped the contact tracks off the circuit board then, yes, someone with the right skills and tools could re-seat it. If you had the skills and tools then you'd have already done it by now, so I'm guessing you haven't. That probably means paying someone to do the work.
It would be a fraction of the repair cost (say 5-10%) to buy and use a HDMI switch on one of the other HDMI ports.