I don't get why you would have the G1100 + a different FiOS Router. The G1100 serves as a modem+router in the same unit. If you are suppose to be getting 150/150 I am sure you are getting your supply via an Ethernet cable from the ONT. At the moment, it is probably connected to the G1100 Modem's WAN port.
Honestly, the first thing I would do is disconnect/remove the 2nd Verizon Router that you have connected to the TC. That leaves just the G1100 and TC. A simple way to test if you would need a new modem would be to actually pop out the G1100 with the Router I just told you to remove.
In any event, if you want to try and fix this issue quickly/directly try my original method. I don't see how you have anything to lose.
First:Find the WAN/Ethernet cable that is feeding your units from the ONT (the Verizon box that the tech installed where the battery backup is). Once you find that cable... plug the end that is currently in the modem/router into the WAN port on the TC (it should be the one right above the power port). Restart and Reset the TC via Airport Utility. You want to create a Wireless network and it should be DHCP/NAT or just DHCP. Do not select Bridge Mode. Also do the usual security key, Router/Station Name, configure if you want 5Ghz, etc. Once all of this is done you should have the TC unit as the direct source for your internet.
If you are getting internet at this point you should run a speed test. I would recommend doing a wired test and a wifi/wireless test. Once you have that done...report back to us! I'll walk you through the steps to connect the FiOS router in Bridge Mode off of the TC.