I agree that there is likely little connection between the loss of the 1st round pick and the recent signings of former 1st round picks. I do suspect, however, that Belichick sees an opportunity for a win/win scenario by signing former 1st round picks to one year deals. If they can perform reasonably well in our system, at the end of the year, they potentially sign longer contracts at a fair rate as a reflection of the positive opportunity they received. If they perform reasonably well, but the Patriots can not re-sign them, potentially another team signs them at an overpriced contract, which benefits the Patriots via compensatory picks. If the player can not perform in our system, the Patriots wish them luck and move on without being under an onerous contract.
I suspect that if the players perform, the combination of the prestige of a former 1st round pick and the prestige of signing a former Patriot will drive up the future contracts these players receive which should hopefully increase the compensation awarded to the Patriots.
Maybe two of the recently acquired picks work out as hoped, one signs a long term deal with the Patriots and one signs a long term deal with another team.