I currently own a 200ft length of main 1/2" climb line and i doubt i'll use the full 200' anytime soon but i didn't want to cut it either. Some tree gear sites offer remnants of pre-cut line left overs, some already with sewn/spliced eyes. Although at this time i currently only purchase from TreeStuff, Wespur has a link on their webpage to purchase assorted sizes of leftover lengths of rope (updated quite frequently) that could be purchased pretty cheap instead of cutting your main line.You could easily find a -50ft length of many type rope there instead of cutting into your main climb line.
I myself ordered a seperate 40ft length of NE Ultra-Vee 1/2" from TS with aluminum snaps and a couple different 8mm prusiks for it to create a custom long lanyard/secondary climb line but i think i'll be buying some 10mm prusiks for the 1/2". I haven't run 11mm yet but i'd think that 8mm access cord would be good for a hitch, you are correct when you mentioned the smaller prusik diameter than the main line. I'm not sure if it applies in this situation but i think it's recommended that the prusik cord be of different brand/make than the rope it's being attached to. I guess it would all be trial & error testing different types of rope together, or you could ask for a recommendation of rope from whatever company you desire to purchase from. I know many have climbers ready to answer any question you may have, i've always had great service when asking any question i've had. TreeStuff, as well as others, also give you the opportunity to buy rope buy the foot also along with the choice of having sewn or spliced eyes with or without snaps and other gear attached for a little more $.
I actually got lucky in a way, i ordered 1 40ft length but it came without the ISC snaps i requested and since it was already spliced on both ends they sent another new lanyard with the snaps this time to make up for the mistake! I love TS!
Good luck & climb safe!