I just checked,. and the Tourney front derailleur is rated only up to 48 teeth, so going above that might be an issue in front.

I do notice at least one freewheel available with a 13 tooth high gear, but it only has a 28 tooth low gear, in case you ever need to climb a steep hill. If you rarely if ever go to your small ring on front, it would possibly work for you. This plus a $10 tool is all you would need to get a higher gear (sacrificing lower gears) Amazon.com : Shimano MF-HG37 Tourney Freewheel (13-28T 7 Speed) : Bike Cassettes And Freewheels : Sports & Outdoors

The difference is that at 80 rpm, your high speed would be 23.7 mph instead of 22 mph

You can play with various numbers here:

Sheldon Brown's Bicycle Gear Calculator