Here are my thoughts on the matter. Perhaps a little bit of a different view, as I'm not really in the camp of "acquire an excellent shutdown defenseman" or "trade away Gardiner". I don't think that the traditional defensive D, shutdown guys is really necessary for good team defense in this league.
The Leafs management has already built a team that is suited for a certain defensive style. Totally revamping this now does not really make a lot of sense. We have a great backbone in Freddy, but we can't just rely on that totally, as we saw this season. One can see the style of defense we need for success on the left side. Gardiner, Rielly, and Dermott. How do they defend? Skating, decision making, and passing. They are effective transition players, moving the puck out of our zone, and into the opposing zone with possession. Problem is, the right side does not exhibit these same traits. Polak, Hainsey, and Zaitsev are not good at breaking the puck out, or navigating the neutral zone. Effectively, each left side D was handicapped by a weaker partner, and made it easy for teams to target a specific player or side for transition play, as there was only one threat on the back end. My solution would be to bring in, not necessarily big name guys, but the right guys, guys who fit into this system, and can do two things well: a) Break out and into the zone, and b) limit opposing teams from doing the same. The second part is where our three left side guys struggle a bit more. Especially at stopping other teams from breaking out by holding the blueline.
So, let's say we have a blank slate on the right side, and Polak, Zaitsev, and Hainsey are all deemed unfit. Who do we fill the void with in the next few years? The most obvious candidate is Timothy Liljegren in my opinion. He is a great skater and puck mover who's a right handed shot. I don't think we need to add in huge names. Look at teams like Pittsburgh, or even Vegas. Without Letang (like in their 2017 Cup win), they have no big name, all-star defenders. I don't think the Leafs need that either. Maybe the solution is already in the system. I see guys like Connor Carrick and Justin Holl, and think that they both might be more fit for these right side roles than Polak and Zaitsev. Maybe not, especially with Holl, but I think it is at least worth a shot. The other name I'll throw out, that will get me a lot of heat, is Martin Marincin. He is superb at limiting entries into the zone, has played the right side with Rielly before, and is an excellent penalty killer. He has done so well in the AHL this season, and I really believe that he could seamlessly replace Ron Hainsey and maybe do an even better job. I don't know much about Ozhiganov, but maybe he is a better defenseman in terms of transition? I'm curious to see him play.
The point is, I don't believe that we need to be trading away Gardiner, and brining in Hamilton or Tanev, or signing Carlson. I mean, it's great if we do, but there might be some much more cost-effective options to perfect a system already in place, that, if it works, can be highly effective, not only in stifling offense, but in producing it for our team. A big part of this is on the forwards too. One thing I didn't see from the Leafs this year was a great use of our speed on the forecheck. Look at how the Lightning killed Boston with their aggresive forecheck. We could do the same, and I think that would help us a lot to limit opposing teams from entering the zone, and give us a lot more possession time. I really like how the roster has been trending more slowly toward speed, with guys like Martin and Komarov finding themselves out of the lineup by the end of the year in favour of young guys with skill, such as Johnsson and Kapanen.
Who knows if it will work out. But I don't think a drastic personnel change is needed as much as maturation, coaching, tactics, and effort from the players. When our forwards use their legs on the forecheck and backcheck, and if we have a defense full of players like Rielly and Gardiner, we could easily become a formidable foe.