Since you referenced me several times in your post, I'll say I support your opinion and stance on this position,
I also see Matthews as the teams franchise building block #1C and future captain.
I like what I'm hearing about out new GM trying to get Auston to lock-in long-term ,and willing to accept he is going to be the highest priced player in the NHL once its signed. Now you accept that and move on even though you know you're overpaying market to do so, He is a unique player and its better to keep then lose.
I think you can fix the Leafs overspending just as you say, trade a winger. For me it would be Marner as he is already overpriced and his next deal only going to be worse still. If you can turn him into a top pairing Dman you make that move. Instead of paying Marner $12 mil on his next deal I'd prefer a $6 mil C and $6 mil top 4 Dman instead.
Nylander coming off his deal allows for a raise to put him in market value range of $8.5 - $9 mil per for a 40 goal scorer and winger for Matthews on the top line.
In 2 years you walk away from the JT contract when it expires, or bring him back only as vet on a significantly reduced deal.
With Auston making ~ $13.5 etc and could be the only double digit player on the team in 2 years time down from 3 now, and you would increase your Cup competitiveness by being able to surround your core with strong depth. Core 4 of Matthews, Nylander, Rielly & another top pairing Dman.