Alternatives to road closures for drive from Trondheim to Bergen to Oslo

So this is a breakneck pace! I assume that you are wanting to drive in order to see the scenery based on your route?
I can speak to several of the legs of your trip.
Personally I would skip Kristiansund - there is literally NOTHING to see or do in that town unless your into the local, dried fish they are famous for. There is a whole museum dedicated to it. The town itself is not charming...the economy seemed to be quite depressed when we were there with many empty storefronts. Just keep driving straight to Alesund...on the way stop in at the stave church at Kvernes and drive the Atlantic Ocean Road. You can do both of these if you get an early start.
Plan 1: If you skip Kristiansund you can sleep in Alesund, then drive the Trollstigen Road the next day, stay in Geiranger that night, take the ferry through the fjord the next day, and then drive to Sogndal.
Plan 2: Like you guessed the Trollstigen Road could very well be closed still...some years it does open early but it's a total crap shoot...for your sake I hope it is! It's one of the best drives in the world.
If not...you can drive to Hellesylt from Alesund and take the ferry through the Geirangerfjord to Geiranger. It's the best fjord to see IMHO! The car/tourist ferry starts operation April 1 so you should be fine. After that you can drive to Sogndal and continue on.
You can definitely do this itinerary but, honestly, I think you're trying to do too much. It won't be restful! Checking in and out of hotels every day and driving for most of each day sounds exhausting to me.

I totally get the desire to see a lot, but I have to agree with Anita that all these one-nighters will wear you down. I would think about ways to condense your route a bit. For example, Sogndal and Flam are fairly close to one another. Maybe pick one and stay there two nights, then explore by car during the day? You might also consider staying in Alesund for three nights instead of Trondheim/Kristiansund/Alesund. Alesund is a great base for seeing the sights in that area.

I did a similarly aggressive driving route in 2014 (Oslo > Andalsnes > Solvorn > Bergen > Eidsdal > Setesdal Valley; I only stayed multiple nights in Oslo, Bergen and Setesdal) because I wanted to see EVERYTHING and I ended up wishing I'd spent at least a couple nights in each spot. I love a road trip and seeing the spectacular sights while driving was part of the pleasure of it, but I still wish I'd slowed down a bit.

Sorry, don't know much about alternatives to closed roads. Good luck!

Based on statistics and travel dates:
Fv 63 Trollstigen, closed
Fv 63 Geiranger – Langvatn, closed
Fv 55 Sognefjellet, open
Fv 13 Gaularfjellet, open
Fv 51 Valdresflye, open
Fv 243 Aurlandsfjellet (Snowroad), closed
Fv 258 Gamle Strynefjellsvegen, closed