Gotta believe if it means solving their QB issue they can carve out some space...that being said if they don't want to obtain a vet because of that or don't want to trade up than this season already has a cap on it and they will still be held hostage by the QB position going forward...and if they honestly think Cam can be the answer after watching him last year than this franchise is in danger of floating into that mediocre world as no amount of beefing up other positions will help you overcome incompetent QB play.
I generally survey lots of different places and sources to gather information (radio, TV, Twitter, podcasts, YouTube, etc.). There are enough people out there that I put some stock into that hear that NE is ready to roll with Cam if need be and that even with him at QB they will be a playoff team. Essentially, with a regular offseason, way more practice time, no COVID to deal with, upgraded weapons, and a better mastery of the playbook . . . Cam would at least be an average starter and the infusion of new players is enough to have them competitive week to week. I get it, that's not your position and I would lean more your way than the other.
The media overall does a lousy job of providing opinions and perspective when it comes to salary cap management. I truly believe that most of them have no clue how the cap works or doesn't work, and if it were up to them they would have the Patriots spending $300M a year.
As far as creative ways to manipulate the salary cap, they certainly can try to do that with guys already on their roster, but they can't control that for players on another team's roster. As already mentioned, they are almost out of cap space for 2021. But they are almost out of cap space for 2022 as well. They have 38 players signed into next year that add up to $174M against a projected cap of $192M. Basically, they have to add 13 more players against the cap (Top 51 contract count) for next year with $18M of room to work with. (Of course they can rework deals to help get there.) And some guys will probably hit incentives that will go against the cap next season as well.
NE hasn't done what other teams have done (ie, adding voidable dummy years to lower the cap hit for this season), so I suppose they could begin to start doing that to stretch their cap dollars. This year, they have 4 players with cap hits over $9M . . .
Gilmore $16.2M
Hightower $12.4M
McCourty $11.1M
Mason $9.5M
We all know Gilmore isn't taking a pay cut, so to reduce his number they need to extend him. If they trade him, they would eat $7.6M against the cap but would net a cap savings of $8.5M for this year. They could save $10M against the cap (while eating $2.5M in dead cap money) to move on from Hightower. They stand a better chance of asking Hightower to take a haircut than Gilmore. McCourty is a much bigger problem, as they would lose more cap dollars by moving on from him than they would gain (so he is a non-starter for mining extra cap room). Mason is signed through 2023, so they could reclaim some cap space by converting his salary into a signing bonus and kick the cap hit down the road.
I am not hearing good things about Edelman, and he likely won't be healthy enough to play until well into the season. He should probably retire as his body is held together with duct tape at this point. They would gain $3.4M in cap space if he were off their roster. Even if he stayed, he would probably be more of a coach and a mentor than a contributing player. In other injury news, there are multiple videos of Burkhead out there showing his progress. He was really productive prior to getting hurt last year. I know he gets hurt a lot be he has been productive when he plays. Worth it if the price is right.
But long story short, there isn't a clear and easy path to freeing enough money to get to $25M in cap space to bring in Jimmy G. (or $18M for Bridgewater). Sure, if they don't want Gilmore and Hightower that would be a decent start (but that would only get them partway there). They would have to make multiple moves to get there. If they start announcing a bunch of moves and extensions, that would be a first sign indicator that is the direction they are going in.