So if my current visa expires while I'm waiting for a decision will I be able to leave the country and reenter?
No, once you have applied, you cannot leave the country, because it will invalidate your application. Also, Section 3C Leave only extends your immigration status after visa expiry while you REMAIN INSIDE the UK. As soon as you leave, Section 3C becomes invalid and you lose all right to live in the UK... which would mean returning to the US and starting over from scratch with a new spousal visa.
So, once you have submitted the application, you cannot leave the UK until your FLR(M) has been processed and you have received your new BRP card.
What do you mean when you said 'find a slot after 1am'? Is this in reference to expediting my application?
Yes. The only way to expedite the application is to pay £800 for Super Priority service, which gives a decision within 24 hours of biometrics.
However, you can only purchase it at the time you submit and pay for the visa, but there are only a small number of slots available each day (I think around 50 or so)... so if it does not give you the option for Super Priority when you try to submit, that means all the slots are gone for that day.
New slots are released at 1am every night, so, what you need to do is log on at 1am and try to submit your application then... hopefully it will give you the Super Priority option. If not, you just need to keep trying each night until it shows up.