frankenbike's frankenbikes

What cassette have you got?
What x7 have you got?
X7 shifters are usually 9 speed, won't have a clutch. You need x7 ten speed.
Or some kinda shimano shadow mech.
I've made this mistake.
A ten speed mech will work with any shifter or cassette. Just remember where your limit is, ie dont over shift on the shifter. Nowt'll happen, youll hear it when you go too far but it shouldn't break off or owt daft

I have two 8-speed road cassettes, an 11-28 and a 12-25.

Derailleurs that I have are a 10-speed X7 (not 9-speed as previously assumed) missing jockey wheels, a 10-speed Rival which I think takes up to 28t, and an 8-speed Microshift derailleur that is currently running with the 11-28 cassette.

The only shifters that I have are the 8-speed brifter Microshift ones.

If youre going drops I kind think bar shifters or DT might be easier to use that bar ends.

Lots of people run bar-end shifters on touring bikes so I reckon I could work with it. I'll only need the rear one obviously. The Shimano shifters (e.g. Dura-Ace/Ultegra 9-speed) can be run as downtube shifters if I get a clamp so they look like a good option.

Those Tektros are essential if you want hoods and V/Canti. MTB and road brakes are diff. At least search 'v-brake road levers'.

I thought cantis worked fine with road brakes?

For the wheel, Id gumtree a bike locally for like £20. Cheaper than the cost of a wheel. Sell everything but said wheel and get a DMR SS kit from that money
32/16 or around that will do you for most occassions.
26 inch wheels are becoming obsolete on new bikes.

Yeah, I'm finding that to be the case. New rim-brake 26" wheels seem to be £100 which is a lot more than I thought. Will have to find a reasonable old MTB and cannibalise it as you say. Might stick with 1x for now and switch to SS later.

I have a sram x?(5 or 7, its low end) shifter. It is 9 speed and 1:1 actuation £6 posted.

All my spare SRAM derailleurs are Exact Actuation unfortunately, so I don't think it'll work. Pretty sure I can find something for a similar price though?

tl,dr:
Buy a donor bike, keep the cassette as an option. Take what you need, sell the remaining parts SEPERATE.
Run it, flat bars. Single speed, whatever MTB brakes are available. Fattest tyres you can get in.

The brakes I've been given are brand new Tektro CR510 cantis - should be perfectly fine I think.

You can get this bike on the road 'free'
Good luck with your stem, it'll come out.

Thanks for all the advice :)