Switching from a 52 to a 53 tooth chanring will not be a noticeable difference, not worth the effort.

Large tooth jumps on the tallest gears are not good, it would be much more usefull to have a 13-14-15 higher end than a 11-13-15 (or something similar). The 28 tooth low gear is pretty low, unless he intends to climb a lot, you might be better off then swapping out the 28 for an additional gear in the high range. Even for a big guy, a 52x13 should be a plenty tall top gear for anything except really fast pack racing.

There is probably no good reason to stay with a 6 speed freewheel on this bike. Go to something like a 13-25 or a 12-23 7-speed freewheel .

11 tooth freewheels do actually exist! I have a rare suntour 11 tooth cog that mounts outboard of the "retention" cog (screws onto the inner diameter of the cog). 20 yrs ago before 11 speed casettes were available, I used this 11 tooth FW on my time-trial bike. Worked well to have the 11 if there was a tailwind or downhill section to the course.