I'm with everyone else on this, you've got to take it. I looked at a bunch of numbers and, as far as I can tell, there is more than one way to get out of the salary issues you'll face next season.
Without knowing whether prospects count against the cap or not (I went with 'not') I figure your cap is running at around 80 million right now, assuming Kulikov signs for around 4 million. That is what Carlson got and I think they are fairly comparable in a lot of ways, in fact I'd say Carlson is worth more at this point. That's a wildcard, but I can't see him getting too much more. If you make the trade your cap would actually go down a bit this year, so that's no problem. Is your league going to adjust the cap if there's a salary roll-back?
Next year is harder to predict, but I guessed and gave everyone with an expiring contract a raise. Stepan and Bailey go to 3, O'Byrne, Cervenka, and Smid to 4, Rask to 6. I don't think those will end up being too far off the mark, but who knows. If anything I think they will be lower, because so much depends on the new CBA. With these numbers you land at 94.5 without the trade and 101.5 with the trade. Over by quite a bit in both cases, so you'll be cutting players and salary either way, almost 20 million if you make the trade.
I'm not sure that you'd need to move Thornton and Kulikov to get under the cap. If you're looking at moving a C I'd look hard at Koivu. That's the weirdest salary structure I've ever seen and it must be a huge headache to work with. On top of that you can really hype the Parise thing. I'd guess he will be worth more than Thornton on the open market, and you can also sell that his salary will drop almost 2 mil the year after next. I'd also try hard to keep Kulikov. He's going to be golden in a few years and much more helpful (and rare) than guys like Smid and O'Byrne. I know that shot-blocking, PIM and hits are important stats, but they are much easier to fill than the offense from the defense that Kulikov will provide.
Chances are you can even get under by just moving or dropping a bunch of other guys while keeping Koivu, Thornton and Kulikov. If you lose Brodeur, Cervenka, Stafford, Smid and Pavelec you'll get under the cap (including all of the other salary increases) if you make the trade for Quick and Stepan. You'd hopefully get assets back for some of these guys, but you can pick and choose a bit to help your cap. You could even move Bailey or Ennis instead of Pavelec. 50 point scorers should be fairly easy to come by in a 12 team league.
Another small point that I think bears mentioning is that Stepan and Kreider could soon form the 2nd line in New York. With Gaborik, Richards and Nash on the top line you can guarantee that Stepan and Kreider (with Callahan?) will be facing 2nd and 3rd D pairing consistently. With the pressure off I think they will be much more productive than we might initially expect. And if the top line doesn't work out as planned then they will have one of Gaborik or Nash playing with them. That's a fantastic situation to be in.
All told I definitely think you should do it. Quick's 7 mil is a big ticket, but the bang for your buck is unparalleled in a situation like this.
16 team, full keeper
19 roster players, 15 prospects
Stats: G, A, PPG, SHG, special teams assists, SOG, FOW, PIM, hits, blocked shots, +/-, W, SO, saves, s%, GAA, shootout saves
C: Crosby, Backstrom, H. Sedin, Boyle, Brassard
W: Voracek, Burrows, McDonald, Filppula, Dorsett, Hudler, Abdelkader, Bouchard, Ott, Zuccarello, Stalberg
D: Karlsson, Letang, Enstrom, Boyle, Giordano, Gorges, M. Stuart
G: Quick, Kiprusoff, Ellis
Prospects: Granlund, Pirri, Caron, Killorn, T. Johnson, Galiev, Corrado, Vatanen, Moore, Rundblad, Bachman, C. Johnson, Desjardins