How much help can my U.S. Senator provide me with in regards to my claim rating?

Generally, a senator or congressperson will make an inquiry into your claim. This normally means a short letter asks the VA to either move your case along or look at a certain aspect of your claim. This can help a stalled claim be resolved, but it won't normally result in much else. After all, this person isn't going to take the time to peruse your claim file and make arguments on your behalf since they are not representing you in regards to your claim, but instead are ensuring that the VA operates efficiently in regards to the claim.

not much till you have exhausted all avenues and been rejected...

I'd suggest an incremental approach. Contact your Congress representative first. I did so when SallieMae was playing games with my school loans and it was fixed quite immediately.