Optimally, to stream 6 cabs, 6 Mr. Videos or some equivalent, 6 capture cards (look into GV-USB2 for decent quality, Dazzle/EZCap for a cheap option), and a computer (or multiple computers) strong enough to handle all 6 streams. If streaming all 6 cabs into one stream, then just use one computer. If you have one reasonably beefy computer, I can help you set up all 6 streams onto it in a way that will work well. Tanner Fokkens sells the Mr. Video for $87 each at facebook.com/snektronix. If you are going down the Mr. Video route, you'll need 6 S-Video or composite video cables and 6 RCA audio cables (extremely cheap on Amazon). 6 of the "yellow/white/red" cables will suffice, but SVideo will give you better video capture quality. Since you are already spending over $500 on Mr. Videos alone for this operation, might as well go for S-Video, as it's only marginally more expensive. Note that if you get S-Video cables, get ones that are either stand-alone cables or have only S-Video and RCA audio cables. The ones that come with composite video connectors combined are usually (although not necessarily) significantly worse in quality.
Here are some random cheap S-Video cables that come combined with RCA audio cables. No idea what the quality would be like on these, but it's probably good enough:
https://www.amazon.com/Monoprice-100127-6-Feet-S-Video-Cable-Molded/dp/B001VL805Y/ref=sr_1_4?keywords=s-video%2Baudio%2Bcable&qid=1580811763&s=electronics&sr=1-4&th=1GV-USB2:
https://www.amazon.com/DATA-connection-video-capture-GV-USB2/dp/B00428BF1Y/ref=sr_1_2?keywords=gv-usb2&qid=1580811845&s=electronics&sr=1-2EZCap:
https://www.amazon.com/Ezcap172-Grabber-Capture-Recorder-Camcorder/dp/B07MDJ73HF/ref=sr_1_2?keywords=ezcap&qid=1580811858&s=electronics&sr=1-2All in all, it totals about $700-$800 (not including the cost of the computers) for a full stream setup for 6 Donkey Kong machines, with most of that cost coming from the Mr. Video.
I'm about a 2 hour drive from there so you can be pretty sure I will go. Is there any sort of prize to the victor, or just for glory?