Personally don't think it'll be that bad for them if they keep Nylander, assuming they can figure how to get under the cap this year. As things stand, if the cap rises as expected, then they'll have something like 33 mil next summer. Let's say 10 of that goes to Nylander's extension, which leaves 23mil for 4 forwards, 3 defenseman, 2 goalies, and 3 healthy scratches (assuming a 23 man roster). That is of course super tight, and not ideal, but definitely doable.
Maybe Brodie takes a little discount and they get him at 4mil, find another top 4 guy for 4mil or less, and a bottom pairing guy for 1.5mil, and that's 9.5mil to shore up the D. Then for forwards, considering the two top 6 wingers they add will get to play with either Matthews-Nylander or Tavares-Marner, they can go cheap here, so let's say the two forwards for the top 6 at an average of 3m, and then two for the bottom 6 at an average of 1.5m, and that puts them at 15.5m added. Leaves 7.5m for the two goalies and the healthy scratches, which is definitely doable. If they can re-sign Ilya at 4m, a backup for 1m, 3 players at 800k, that's 7.4m, bringing them just under the cap.
While that's obviously not an ideal situation, it's just for the one year, and then Tavares is off the books and 11mil more frees up, and then they can really try to balance out their lineup.