I would have played it as the best teams in the NHL do.
They determine in-house what any given player's value is - on their roster, in their pipeline, and around the league.
They begin a negotiation low, and move toward that initial evaluation. That initial evaluation is the drop-dead, walk-away point.
If another team is willing to pay more, you do not break from the internal evaluation to out-bid them. You let the other team over-pay and keep your powder dry to ensure you have the assets ready for the next big name to hit the market.
You move on to your contingency options, which will almost certainly cost less. Because you would rather improve your team by a little with surplus value, than improve your team moderately at negative value.
Good teams don't let the market dictate their moves. Bad teams let the market dictate their payment.