Best mesh extender for c3700 router? (e.g. EAX20? EX8000?)

Your primary issue? the C3700 and distance.

An extender has to run off what the route is capable of.  So if you're starting with the C3700 which is a N600 device (300mbps-2.4ghz and a 300mbps-5ghz) you're already starting at a lower baseline. Plus link speed isn't the same as throughput (actual speed). 

The other issue is that standard extenders (not triband) have to receive and then retransmit a signal. And they can't do both at once. So it cuts throughput in half of what you had. Which isn't the best with the C3700. 

The triband extenders help negate this as they reserve 1 5ghz radio just for router----extender communication. this helps stop that speed hit. And they work well. But again, they can only go as fast as your router can. So you'd be maxed out at the 300mbps 5ghz link speed. (throughput is roughly 55% of what link speed is for 5ghz) 

So you can buy a AX extender but you're not going to get the benefits of an AX device because its having to link through to the C3700.

Options that I'd consider using? 

1. consider an upgrade to netgear orbi. the RBK43 and RBK50 sets can be found on amazon for pretty cheap renewed. this would upgrade the router and give you a satellite or 2. You'd just put the C3700 in modem only mode and use it as just a modem with the orbi handling routing and extending.

2.  Look at the EX7500.  Its the base model triband. You could also consider the EX7700 or EX8000 but you wouldn't see a performance difference without upgrading your router. 

3. Consider powerline setups like the PLW1000 or PLW1010. Not all homes function well off powerline because many things can influence the powerline network but it'd potentially let you run a powerline run to where you wanted that had a wireless access point at the end. It doesn't function as a mesh but it'd give you another access point.