How can I use a 15A momentary switch (switches) to replace my multi-button wall-mount garage door opener?
You may be overthinking this.  

For controlling the switched-with-door fluorescent/LED lights, the opener already has a sophisticated way to do that which works with the remote. Start at the opener itself.  Screw a NEMA 1 to Edison adapter into the lamp socket. From there, 2-prong plug and cord up to metal conduit, where you either have an inlet or strain relief. From there, the conduit goes to each lamp location. You also run a ground wire to a viable grounding point since the source has no ground. 

If you don't like that plan, consider the GE RR7 relay, which takes a 24V momentary pulse to throw the lights on or off.  It is specifically made and listed for lighting.   However if that is not the same voltage your garage door opener runs on, you will need more relays. 

For the garage door opener buttons, contact the factory.   Since garage door buttons are low voltage wiring, you are free to improvise.  Also if you count your buttons and there are one more wires than buttons, it is not using resistance etc.