Not an issue, since this is a cash-out refinance they can just drop the loan amount to 80% of value to avoid PMI (assuming it will still be a cash-out refinance with the new lower loan amount of course). Don't have to start all over. Case like this would be a change of circumstance and you'll get a new GFE emailed, etc... no biggie.
Regarding lower rates, talk to your loan officer about it...some can and some can't change rates...depends on the lender/investor. I can lower rates, sometimes free and sometimes for a small fee...depends on market conditions. Policy is in place so that we don't lose customers when market drops.
Hope that helps.