Answer: pretty weak! But their weaknesses are simple and could be easily overcome by future design.

But Jason's Finest Crew was tromping along at top speed. (It helped that I kept forgetting to throw tribbles at him.) He was tied down for a good long while by a pretty effective Buried Alive / Murasaki Effect / Founder Secret combo, but cleared dilemmas at another planet mission (without solving) just as Murasaki ticked out. In my favor: he needed to use nearly all the Enterprise's RANGE to get both missions solved in one turn, so I planned to use Nilz Baris's special download of Incoming Message - Federation to force him back to his outpost. Incoming Message - Fed would actually give me the win for the first time in one billion years! But, when the moment came, it turned out that Nilz Baris was dead: killed by Denevan Neural Parasites on the previous turn, and me without the ability to re-report him (even with Nanoprobe Resuscitation). Alas! Jason finished his missions unmolested for the full win.

Joe asked me to be unsparing, so I played Tribbles on him to their fullest effect. Never did get a group over 1,000 tribbles going, but hey, that was still enough to annoy.

My draw engine broke down -- I just couldn't draw any Temporal Shifting -- so I ended up play 1 / draw 1. Like a GENUINE FOOL, I didn't use Temporal Conduit to get Temporal Investigations to get extra draws during the early part of the game, when Joe was playing [AU] personnel every turn, but I did eventually go over and use Visit Cochrane Memorial for draws.

Joe had a truly massive team put together, but was hesitant to send them into risky missions, given how alarming modern dilemmas can be. An understandable impulse! And lucky for me, since it bought me some time while he cautiously assembled his men and then drove them into a Cytherians. (He was on a RANGE 14 Future Enterprise, so it didn't last long.) His own combos were strong, and kept killing Chekov and Scotty, which made the Starship Enterprise almost unflyable, particularly on a mixed spaceline (we alternated almost every other mission). In the end, I was able to clear all the dilemmas at both Clash at Chin'Toka and Ag Assessment. (We both seeded Clash, but Joe wasn't able to steal because he lacked one of the skills on that particular team.) But, as time was called, my Enterprise (with 6 RANGE) was at Ag Assessment, 3 SPAN from Clash, picking up the personnel needed to solve Clash. With a bit more RANGE (or perhaps more ships), we could have solved Clash, dropped Genesis, and doubled Ag Assessment a turn or two earlier, but the Enterprise spent so much time on milk runs back to Sherman's Planet to pick up personnel that it just wasn't able to make it work. So, instead, to secure the mod win, I solved Sherman's first and then flew over to Clash to finish there.

All in all, a nail-biter of a game, close-fought to the end, and, again, Joe was a pleasure to play with, and I look forward to seeing him at future events!

Hobie stole my deck, then beat me with it. Fair's fair!

I was, once again, play 1 / draw 1 for much of the game, and Hobie did a thorough job using Gold to repeatedly murder my dudes. I refused to give back Gold, since it would give Hobstar the extra points to make Luna a 35-point mission (securing him the win). But this meant he just kept on killing key dudes right to the end of the game, far far faster than my bad-drawing deck could replace them. Again limping back and forth between Sherman's Planet and Clash at Chin'toka, I was not able to solve any missions before the end of the game.

Oh, also, Hobie's Enterprise NX-01 came over and blew up the Starship Enterprise.

Twice.

But I did have the satisfaction of refusing to accept Hobie passing me Gold! until he said the words "Where's the vault?" And my tribbles were terribly annoying. So, all in all, still quite a fun game, despite the final scoreboard.

However, this is complicated by the fact that [OS] is already quite good with help from Mirror Quadrant and 24th century cards (especially [AU] ones), and, since the [OS] cards are all part of existing affiliations (unlike Starfleet and Vulcan), anything you give to them may end up stacking with the many toys those affiliations already have. It would be reallllllly tricky to give [OS] [Fed] an extra free play, for example, because any free play you give them would instantly be incorporated into the Alpha Quadrant Voyager Free Report Salad deck that's been going around. So this will be an interesting puzzle to crack. Personally, I wouldn't mind seeing some Crossover hate in TOS block to discourage the casual supplementation of non-Mirror decks with a sprinkling of Mirror personnel... but that covers only half the problem.

EDIT 17 July 2019: For anyone who still wondering: yes, I played this deck at this tournament because, at the time, I had just secretly been added to the design team for The Cage. And, yes, my "closing thoughts" here were really a first draft of a design goals document I submitted to the rest of the team. The influence this ultimately had on The Final Frontier, To Boldly Go, and some of the personnel is fairly obvious, although there were 18 months of changes before we managed to pin everything down.