The problem is that you can spoof Google location tracking and other systems that actively report your location, but you can't (AFAIK) spoof your cellular tower data.

I don't know the level of difficulty involved in the former, but "spoofing" cell data is possible by making the phone connect to sub-optimal towers. This would cost you service quality and battery life, but you'd "appear" elsewhere. This requires reversing and patching proprietary software, though.

The cell towers save the round trip time of each ping. This means that even if you connect to a far-away cell tower (which you can actually do just fine with a long metal cylinder and a kettle lid, no need to mess with software), they will be able to tell you were not near the tower in question.

Is the RTT really dominated by lightspeed delays and not processing in the phone?

The processing in the phone can be reliably removed from the equation using simple statistical methods.

Not unless a software patch on the phone introduces significant random variances into the RTT. But yeah, there will be no pretty way to make the network "think" you are actually near another far away tower. I bet, however, that this is still possible using a vulnerability in the "ping" method itself, like not sending a random nonce for authentication of responses (so that I couldn't send the "pong" before receiving the ping).

Are there any phones that currently do this?

Create a fake tower like they do to illegally intercept cellphone calls?

That doesn't make sense, the data from that fake tower won't be used in court.