I assume that Army has a decent idea of Tarasenko's list and I wouldn't be surprised if Tarasenko has given him a firm "I'll go to these X teams" list. However, if I were Army, I wouldn't be limiting my search of trade partners to those teams. I'd be shopping him all around. If I wasn't getting interest from his approved list and I found a taker from a team not on his list, I'd be more than comfortable trying to convince him to expand his list by saying something along the lines of this:
"none of the teams on your list have made a realistic offer. I've been working on it all summer and this is the only offer I've gotten that I'd consider taking. I'll continue entertaining offers through the year from teams on your list, but after today, I'm done actively shopping you. If you want off this team, you need to waive to facilitate this deal. If you don't want to do that, then we are excited to take one more run at the Cup with you in 2022/23. If I'm asked by a reporter, I'm going to tell them that you vetoed a trade away from St. Louis and make it clear that we consider the trade request rescinded."
Put the ball in his court and let him make the choice.