Double checked the schematic and it looks like J120 and J121 are 11 pin connectors (0.156"): (Great Plains) CS156-11-LR. The Keying pin part number is 15-04-0219.
I would get both size trifurcon connectors: 0.156" 18-20AWG 08-52-0113 (Great Plains) and 0.156" 22-26AWG 08-50-0185 (Great Plains). Maybe get 100 a piece and get that 15% discount? Going by the picture I believe the 22-26AWG contacts would fit nice.
Of course you'll need a crimper and I found this one to work a dream: https://www.amazon.com/gp/product/B007JLN93S (HT-225D)
Lastly you'll most likely want to replace the headers and the part number is 26-48-1245 (Great Plains)
As lyonsden mentioned you may want to invest in a desoldering tool. You either can get the real deal Hakko FR-300 or the knock off Aoyue 474A++ https://www.amazon.com/Aoyue-Digital-Desoldering-Station-Built/dp/B00ABJ4AEC/ref=sr_1_4)