Just my 2 cents, make sure the gas cap has good airflow.  Clean out the keyway.  Could be that when you are really pulling fuel, like highway speed, the air intake from the cap can't keep up and sets up negative pressure in the tank.

You Know you have a crap petcock.
Fix that.
Problem solved?
Good.
Not solved?
Keep going.
Tank full, minimum air gap, low pressure develops quicker than when the tank is low.
Either way, a run for sixty won't cause your tank to starve the carb..

Details about the peacock
Details about what the bike is doing

Sorry for the recent post that told you all nothing. I was feeling defeated. Lol. But guess who is riding?!! When I put the rapture petcock on it fired right up, then things went south...very south. At the time I last posted I didn't  know what the cause was, but, All the sudden, it wouldn't start. Cam chain tensioner came apart. It  wasn't damaged, didn't see any damaged  on plates or teeth (thank goodness). I had a buddy of mine weld a washer to the tensioner. This poor girl can't afford the one they sell. When he said he'd have me riding by morning, I thought I was home free. What that really meant was I was going to spend the next 12 hours (maybe it was more) with him walking me through doing everything myself.  So guess who learned to adjust a cam chain! Nightmare. Learned to check my jets (one was clogged), The sun was almost up, I was hungry, frustrated almost to the point of tears (hey I am still a girl. Lol), and something amazing happened.... I finally got to ride my Savage! All smiles!!!
It's and old bike, and I know it's going to require constant upkeep, but I'll get through it again.
I just wanted to say this is an awesome group of people! I searched this site and learned sooooo much from you all putting things in plain English. I went here first, Clymer second. Lol.

Let me clarify... When I said adjust can... I no there is no technical adjustment for it. I manually worked the chain over three teeth. Which may not be the right way but it worked.

Any suggestions about a muffler? Or any way to make this thing not sound like a hopped-up four wheeler  

Avoid the ones that don't mount with a rail and the ones with a crossover. I've heard that the Catalytic ones work okay.

Jenn C,If it makes you feel any better,the nearest town to me( 25 miles )is Boonville N.Y. and is about 1/4 the size of your town.I did search and found your elevation to avg .about 500ft above sea level ,the rest of your state (north ) to be between that and 1000 ft. I run a Dyna muffler,with a stock motor using the stock 52.5 pilot ,3 #4steel machine washers for the spacer mod,(to raise the jet needle,which I highly recommend) and a 150 main jet . I lived in central and western N.Y. at about 450 ft and found these settings to work very well with a Dyna.the bike will run smoother ,and a bit more powerful ,I'm sure it will put a smile on your face.many owners have been amazed at the difference lifting the needle jet a few thousands can do. You need to be careful the screws in the carb are J.I.S. -Japanese Industrial Standard ,and phillipshead screw drivers are too pointed to fit fully down into the slots,so tend to strip the screws X shaped slots,and the small screws down inside the slide to do the spacer mod are soft brass.