We've been trying to do the sustainable meat thing. Building a plucker was the best idea we've used since getting chickens! Seriously, processing day is pretty laborious, so every other month sounds like the best option. It's taxing in more ways than one, so NOT having to pluck by hand is a HUGE plus. We built a "whizbang" style plucker and now de-feather each bird in 15 seconds or so. End costs were around $400. That's a lot of money (even though you only pay it once)... so if you're only looking for short-term cost savings, buying chicken from the store might still be the best option, BUT if you plan on regularly processing chickens there is no better time/effort saver. Plus, $$ can be saved if you already have materials, which we did not.
When we were planning, I made a YouTube playlist of other pluckers or inspiration here: https://www.youtube.com/watch?v=tL4x6ja1jBg&list=PLxSuAiPiDXaZDkktE5q3d5bSO0eCgXiZZ there are lots of different modifications people have made that are just great and make the plucker even better.
Oh! Also, I wouldn't mix CX with your current flock, as they will be coming from "factory" conditions and who knows what they may be carrying at first. I've also had zero luck mixing chickens of different age groups, so a divider may be necessary if you raise them in your current run (which sounds big enough for 10 additional birds, for sure).
If you want exact numbers (exactly 10 birds for instance), I would recommend getting a few extra CX to account for potential losses. CX can sometimes croak for no apparent reason. If you end up with too many at week 8, you can always gift/sell the extras to friends and family (we did, it was a hit!). Good luck!