The 16-tooth jump in chainrings is close the the max for good shifting, and may be all your rear derailleur can take up. If you go bigger with the large, would you be okay losing the lower gears? And you'll need a new chain, of course.
You should be able to find the max chain wrap specs for your RD--look up the part number on the inside of the body.
175 cranks is probably right for your height.
It's hard for me to imagine the value in a $100 upgrade but I'm just a recreational rider.