The 2200G comes with the Wraith cooler, which I believe is actually pretty good for a stock cooler.
So you should be able to get away without the Coolmaster, saving some additional cash :) [Unless your prices are CPU only]
Edit: You would probably need to put the savings into a PSU though!
It's not quite that expensive. I paid less than $200 a few weeks ago for 32GB of SODIMM to go in a NUC. I think $300 for all the guts of a machine is probably pretty optimistic, but the RAM would only be about a third of it.