The entire idea of a sign and trade from Tavares' perspective is that there is the same bidding war but on an 8 year deal instead of 7. For example, let's say the 'UFA bidding war' drives the cost to $14 mil AAV at 7 years for a total value of $98 mil. Tavares then makes it known to all the teams he'd be willing to sign with that $14 mil is an exceedingly fair number and that he'll accept a deal with whatever team is willing to do a sign and trade where he is making $14 mil AAV for 8 years instead of 7. That's $14 mil more for Tavares, which is by no means trivial.
From the player's standpoint, this isn't about taking a lesser AAV over 8 years instead of 7. It's about getting an extra year at the same/similar AAV. If Tavares is open to the sign/trade idea, it is because he is trying to maximize his earnings by either getting the same AAV for an extra year, or coming down slightly on the AAV in order to reach a grand total that wouldn't be feasible under a 7 year deal.
Any argument based on maximal earnings needs to consider his next contract as well.
He'll get a better deal on his next contract if he's negotiating it at age 34 than he'll get at 35. At the very least, he'll almost certainly be making something significant in that age 35 year, regardless, so it's not $14 million or nothing...it's $14 million or whatever he gets in the first year of his next contract. That is still going to be high number, probably $8 million at least.
Let's say he plays through at 38 and look at some hypothetical (but plausible) frameworks for his next two contracts covering that span:
14 x 8 plus 7 x 3 = $136 million
14 x 7 plus 8.5 x 4 = $132 million
14 x 6 plus 10 x 5 = $134 million
All those scenarios end up pretty close in total value, so in which one of those scenarios is he in the best position to leverage additional value above what is predicted if that's his desire?
IMO, he can most easily do that by taking a shorter deal now and attempting to negotiate another monster deal at age 32 or 33, when he'll still have enough high production years left that he can easily command a hefty AAV, and there will still be enough suitors that he can ask for (and will receive) a near max term contract. He won't have anywhere near the same leverage or market if he's attempting to negotiate his next deal at age 35, especially if his play is already starting to show signs of slipping by then.
You can argue that getting more money up front means more security, but when you're already banking $70-84 million even on the "short" contract, security isn't really an issue.
I guess my big points here are that the extra year at $14 million still likely isn't all that valuable in the grand scheme of things, and arguably isn't his best path to maximizing his career value if that's ultimately his primary focus.
Here's something to consider: Would you rather make $88 million and live/play at your top choice, or make $100 million and go someplace that is less attractive to you? Does that answer change if you've already made $44 million?
At some point he is probably going to reach a place where other factors start to matter more than milking every last dollar from the stone, if he isn't there already. We tend to ignore that in conversations like these, but I think more often than not these uber-compensated athletes start to care about a lot more than just the dollars involved. They want to be happy, and that often involves things like playing where you want to play, living where you want to live, not having to deal with unnecessary stresses, and generally controlling your own fate.
Is there any real incentive for Tavares to pick from the teams that are willing to do an 8 year sign-and-trade if his top choice among anticipated UFA suitors isn't one of those teams? I don't think there is, personally. I just don't see the offer of an 8th year being a strong influencing factor on where he signs.