I've come up with a solution. It does assume that play can be resumed, hopefully With fans allowed to attend, by November.
So in early November, you resume 2019-20 Season play where it left off. You try to rework the schedule, playing roughly 50-75% of the games previously planned, concentrating perhaps on those with less travel involved, and with more relevance towards the Playoff standings. Focus more on those teams on the bubble of making/not making the playoffs, since they have the most to gain/lose.
Finish by Thanksgiving, and then take a few days off for the holiday. Resume with the Playoffs, under a much tighter schedule, doing lots of back to backs, which are usually avoided. If possible, finish the 1st 3 Rounds by Christmas, although that might be tight.
Come back after Christmas with either the 3rd Round, or the Stanley Cup Finals. Schedule one of the Finals games on New Years Day. Go back to an every other day schedule, and wrap the Finals up by January 10-15.
Take the rest of January off. Everything resets. Open Free Agency and allow Trades. Open Training Camps by February 20. Play a very abbreviated Pre-Season schedule. Start the "2020-21 Season" by March 5. Play a shortened season, roughly 60 Games, concentrating on Conference matchups, and less travel. Perhaps make the games against teams in the other conference Once only, like they have done in prior years. Finish the Regular Season by the end of June. Repeat the prior season's playoff model, awarding the Stanley Cup by mid-August.
Well, that's my idea. I just don't see how they can resume a game with as much physical contact as hockey, until the current situation has calmed WAY down. You're going to see a lot of athletes, in all different sports, who decline to put their well being in danger, if the virus situation is still unsafe and tentative. I think Baseball is in a much tougher position. Their season was on the verge of starting, and they Need to play Outdoors, and are extremely sensitive to Rain. Although Hockey in Summer seems bizarre, it is not impossible, whereas Baseball in December in New York, is a fantasy.