Retaining must be out of question, since it would have an impact for eight years. That makes cap dumps necessary parts of the deal, regardless of who would be acquiring Price.
To be honest - Price is not moving. He did not sign that contract by accident, and neither did the Canadiens. His NTC is already quite limiting, and when the full NMC kicks in next summer, that's when moving him becomes impossible. He ticks so many boxes in terms of what teams would not be looking for in an asset - age, woeful amount of term, sky high cap hit, even higher salary, crazily high cost of acquisition (we'll get back to this soon) and a concerning injury history (for a goalie, that is). That comes with half-decent goaltending, but if, for some reason, you don't get that from him, then what?
If, however, Montreal decided to cut the cord and explore every possibility of getting rid of the guy, there's a big obstacle right after the beginning: how high a price do you set for Price? If you value him based on how important the guy is for Montreal, you're getting thirty nos as answers and will be left empty-handed. I have a hard time seeing Bergevin not doing that: he knows how important Price is to his team (which is shown by the massive deal he gave to Carey), and honestly, who would not? Instead, Bergevin needs to lower his expectations by a mile. Given the right circumstances (=flexibility in asking price), Price is able to fetch good assets. Those assets just won't be what every Habs fan would want: no young stars would be made available for him, and neither would current superstars. How about blue chip prospects? Sure thing. First rounders? Yes. That might be aiming low for someone who has recently won the Hart and is renowned for being the best one at his job, but if aiming higher results in a guaranteed miss, why bother?