Broadlink or geeklink, both won’t work. They use UDP instead of HTTP protocol. Sorry to say this is end of the road for broadlink and geeklink solution.
You need to look at your Hampton Remote, check it against FCC database. If it’s showing 433, 434, or 315 it would be compatible with Broadlink. if it’s other than those frequencies, then you’re out of luck
You can try this if you don’t mind on getting your hands dirty by building a 433MHz bridge