Firstly, I don't know what your specific situation is, but it sounds like what you're trying to do might be illegal. You're potentially messing with people's emergency services (911 access) and Verizon might own the cable you're trying to mess with. But, I'll assume you've worked this out somehow, and take no responsibility for your actions.
I used to work on telecom and have done cutovers on live copper. It's easy; much easier, but dirtier, than fiber.
Moving to a larger gauge wire is not ideal, mainly because splicing it together could be less reliable (the UR2 is designed for the same gauge wire), but otherwise will not cause any issues.
Using a temporary connection while cutting over is standard practice. We used some vampire clip jumpers (AKA ABN (Angled Bed-of-Nails) clips) to make a temporary bridge, cut out the old, made a new splice in the middle. The gel inside the UR2 (icky-pic) is to keep water out, not act as a conductor, so the vampire clips are just as good in the temporary situation. If someone is talking on the phone during the cutover they will probably hear something, but should not be too disrupted.
I encourage you to check the law on this. If you don't have permission and licensing then even if you're not caught in the act and Verizon later finds out someone illegally performed the exact thing you already got a quote for... Well, it's still illegal and they have a damn good idea who did it.
Best Answer
DSL filters are used to prevent voice communications from affecting the DSL (data) signal and vice versa. Typical home phone wiring is a combination of tree (each jack connecting separately back to the network interface (that's phone company terminology for the "main connection", NOT necessarily anything to do with your computer network per se) and daisy-chain (cable from network interface to one jack and then another cable from that jack to the next jack). Bottom line: DSL handles open jacks (no devices connected) just fine and only needs filters on the jacks connected to telephones, answering machines, fax machines, etc. Never put a filter on the DSL modem itself - the DSL modem includes a different type of filter internally.
I typically wire up a filter at the network interface, after splitting to a separate cable for the DSL modem, but most people don't do that. End result: put filters where you need them and not where you don't. If you ever connect a phone again at that location then you can either put the DSL wall-plate/jack back in or use a regular inline DSL filter. If you were to ever connect a phone without (re)installing a filter, there would be no damage, but your DSL connection would be degraded (slower or not work at all) until you install a filter or disconnect the phone.