K will simplify
New rear wheel with a fixed gear hub and possibly a new crank / bottom bracket. if the BB is french threaded (and I'm no expert on timelines by any means but I think the carbolite models should be english) it will be more complicated, not impossible but the only two places I know of that make french threaded BB's are Velo Orange (Cheaper) or Phil Wood (Very high quality, but very expensive) Although if its a double you will most likely beable to reuse your crank, in that case you will most likely need a new shorter set of chainring bolts

Don't take the brakes off and get some toe cages too