The problem with allowing Brown to walk in FA next spring is that it would happen in March. While Wynn may have begun working out again by that point, it seems unlikely to me that the Pats would have any certainty about Wynn's ability to be the starting LT for Wk-1 yet - if that was ever their plan to begin with.
From the little I've seen of Wynn with the Pats, augmented by college tape and media reports (taken with a grain of salt), it appears that Wynn is likely to be a starting caliber OL, if/when he's recovered from the Achilles injury. And he appears to have considerable positional versatility - IOW, he's not locked in at LT, and he might be a replacement for either Thuney or Cannon, ultimately.
Thuney's rookie deal runs out at the end of 2019. It seems to me that he's been at least adequate, most of the time, but Wynn may be an upgrade.
Cannon has been a very good starting RT for the Pats since he assumed the role in mid-2015 - when he's been healthy. From 2012 through 2016, Cannon only missed 7 games due to injury Then, he missed 9 games in 2017 with an ankle injury, and most of 2018 Camp with an apparent calf issue. It's not really possible for us to be certain if this has been merely a run of bad luck, or if it's the beginning of a trend. Cannon turned 30 in early May, which means he'll be 33 going into his contract year of 2021 (which is also Wynn's contract year).
To complete the OL contract picture ...
-- Andrews' second contract expires at the end of 2020
-- Mason is now signed through 2023
-- Karras appears to have become the primary backup for the IOL. His rookie deal also expires at the end of 2019.
-- Schwenke also seems to be a capable IOL backup, but he's FA at the end of this season.
-- Waddle, who's been mostly adequate as a sub at RT, is also FA at the end of this season ... and the Pats really don't seem to have another OT backup at the moment, certainly not anyone of long-term starting caliber.
Give the Pats' typical draft slot, they really don't get a shot at starting caliber tackle prospects every year. Even if the 2019 draft class for tackles is strong, the chances of one falling to the Pats may still be fairly slim. Even then, a very good draftee may not be ready to start until 2020.
Given all the above considerations, I think it would be in the Pats best interest to attempt to extend Brown as soon as they're certain about him.
There are currently 10 LTs under contracts paying a nominal APY of $12M or higher. Mason's new nominal APY is $9M, which ranks him 9th among RG and 11th among Guards overall. In 2016, when Cannon signed his current deal, his cap hit was 4th-highest among RTs, but his nominal APY ($6.5M) is now 10th highest among RTs.
Brown's current salary/cap hit is $1.907M. That's the same as Mason was making for 2018 before signing his 5-year extension - which increased his 2018 cap hit by $1.5M. Assuming that the Pats see Brown as their long-term LT, an offer of five years at $11.5M-$12.5M seems reasonable. If his agent wants to hold out for significantly more than that, it would create a problem.