Then there has to be something wrong with the old receiver. Either it's broken somehow or it's not 315 MHz or both. I haven't seen any of these units with the squiggle trace. That is used on 2.4 MHz devices and about that same size.
I guess I had the impression you wanted to use this with an existing garage door opener. I guess not. At least not with the receiver. I guess that's why you were looking at using the walkies.
Every unit I've seen uses the coiled wire for an antenna. Don't know if you can get that to fit in the transmitter case. You can buy them online, but they are just copper wire coils which you can make yourself.
That will either be easy, or a big PITA I expect. They sell receiver modules with relays which I'm sure you will need for that. Maybe even another relay controlled by the receiver relay which may not be up to switching much current.
I don't recall the details of what you are controlling, etc. The thread is so long I can't find it. I did find in your original post where you referred to "I have an add-on garage door opener". That's what made me think you were talking about an existing receiver on a garage door.