First, I would try to sell JT on the core, and current younger supporting cast, like many have said.
He's never had 2 top 20 defensemen on his team. He's never played with a truly elite scorer like Tarasenko. You could argue he's played with guys like Schwartz and Schenn on the Islanders, but most of the time, those guys have been on his line. Contrary to what some believe, I think the drafting of recent years has shown that Doug Armstrong wants this team to get younger, faster, and more skilled up front. He has a vision of a quicker, more swarming style of hockey rather than big body checking.
Second, I'd sell him on the lifestyle here in St. Louis. How often players stay after retiring. The cheaper tax rates. The easier media situation. A better family atmosphere at the rink, etc.
Third, I'd circle back to him being the missing link between the Blues being a playoff contender and a Stanley Cup contender. He pushes them into true Cup competitor territory. I'd give him a projected lineup next season, after a few off-season moves have been completed.
Fabbri Tavares Tarasenko
Schwartz Schenn Kyrou
Steen Thomas Thompson
Barbashev, Brodziak Soshnikov
EXT: Sundqvist, Jaskin
Edmundson, Pietrangelo
Dunn, Parayko
Bouwmeester, Schmaltz
Bortuzzo
Husso
Allen/Hutton/FA
I'm not saying he'd pick the Blues, but it would be hard to argue with a group like that. It's faster, more skilled, and has a decent mix of rookies, veterans, and your core.
EDIT: I forgot about Barbashev. Thorburn can be waived or let go for all I care.