It actually makes quite a bit of sense to expect this negotiation to drag out until some logical deadline before being completed with a signed contract. Here's why it makes sense for both sides to drag this out...
1) Chevy doesn't have any time pressure now - In some situations a GM has some pressure to complete some contracts before moving on to others, either to set some parameters around internal salary structures or to manage cap situations. Trouba is Chevy's last contract so he doesn't have any pressure to finish Trouba's contract before sorting out others. In addition, Trouba isn't scheduled to even skate with the Jets for several weeks with the upcoming WHC, so the Jets aren't losing anything without having Trouba signed. In fact, the WHC will replace training camp in terms of getting Trouba sharp and in game shape. The only way for Chevy to really rush through the negotiation is to start bidding against himself, basically increasing his existing offer without any impetus for doing that. With no pressure on Chevy, he can wait until the pressure increases on Trouba which would be a more likely time to get the best deal.
2) Trouba will get his best offer closer to the season - I expect that Chevy has already made some offers to Trouba (various terms and salaries). These are now set, since it is highly unlikely that Chevy would contemplate reducing his offers. So at this point there is only upside for Trouba to wait until Chevy has a bit more incentive. Chevy's offers can only go up. The worst case scenario for Trouba is that he accepts one of the offers already on the table. So why not wait and see Chevy's best offer?
My guess is that this will drag out until there's a critical balance in terms of pressure on both sides to get a deal done, when Chevy is inclined to give his best offer and Trouba's bargaining power is at it's peak.
My guess is that it will either be just before the WHC or just before the Jets regular season begins. Once the season begins, Chevy is most likely to "fix" his offers so that ongoing delays in signing won't help Trouba, and will actually start taking money out of his pocket.
So, if both sides are looking toward a long-term deal, I expect it not to happen until we are closer to the regular season.