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Some more ideas:
Unless you specifically want that posh Halo wheel, here's a budget one: https://www.ebay.co.uk/itm/26-DISC-BRAKE-ONLY-MOUNTAIN-BIKE-WHEEL-REAR-CASSETTE-FITTED-7-7M-8-9-10/254349298641
I'd go for more gears. My experience is 9 is still a bit gappy but 10 isn't. You haven't mentioned shifters, so are you using the shifter on there?
Shimano XT 9-speed derailleurs are that sort of price, compatible and
have more kudosmight be better.Just for reference, I got a new SRAM X7 rear derailleur for about £35 and a pair of matching 2x10 shifters for about £35. It's a matter of trawling the eBay shops but I appreciate parts are a bit short on supply at the moment. Also put a wanted ad out for this stuff on Retrobike.
Right, here is what I am considering:
Halo T2 rear wheel : https://www.ebay.co.uk/itm/142715036686
8 speed cassette : https://www.allterraincycles.co.uk/shimano-claris-cs-hg50-8-speed-cassette-11-32t-
Shimano Altus M310 7/8 Speed Rear Derailleur : https://www.wiggle.co.uk/shimano-altus-m310-78-speed-rear-derailleur
https://www.decathlon.co.uk/p/hydraulic-braking-kit-complete-front-or-rear-160-mm-tektro-auriga
https://www.decathlon.co.uk/p/3-to-8-speed-bike-chain/_/R-p-331640
That brings it up to about £195 so far. How much are the replacement dropouts for the Bullitt?
Might have to sell some other gear.