A very inexpensive option is to use 8 of 9 OR 9 of 10 cogs on the 7 speed body.
All you'd need is an X speed cassette, remove one cog and use an X speed chain.

Since you can use friction shifting, you don't need those pesky, expensive new shifters that you don't use 1 speed on.

It appears your hub is Uni Glide/Hyper Glide compatible.

I'm thinking that hub won't take an 11T cog. 12T or more.