I don't get why people buy new parts altogether just to avoid simple wheelbuilding jobs. Wheels are not complicated things. I'm no master mechanic, but I've built a number of wheels, and reworked old wheels, with no problems whatsoever. I'm not even sure that you could take out that much misalignment with a new bottom bracket, and if you did it would be a workaround, not an actual fix.
So, you can certainly buy a new rear wheel, crank, cog, spacers, and bottom bracket if you like, but if it were me I'd spend $15 on a spoke wrench and a cone wrench and fix what I had.