Full timing a three season camper in Alaska sounds like a real experience, not one I think I'd be up for, but I compliment you on your willingness to get out there and do it.
Full timing it in Euclid on the south shore of the lake likely came with its own challenges, I suggest AK will be related, but an entirely different animal, particularly where you might be heading. Get too far up, and you'll run out of day (it's currently night up there above the arctic circle - but that's WELL north, just above Seward Pen). Seems like you might be down where the action is. Where are you headed?
Considering that you are convinced to do this - and recognizing that this is just spitballing on my part - I might consider:
1. Think about a different camper or plan from a $ standpoint.
From Euclid, you've got a 4-5,000 mile haul ahead of you (to Anchorage). Fuel and towing cost, plus time, will add up - how does it compare to leaving your rig, driving and finding housing. Roads have places where they are downright nasty (not even accounting for weather). If you sell your trailer now, can you pick a different one up closer to (or even AT) your destination? Or, as Tom suggested, ditching it all and flying? Seems like getting there will be an enormous task in and of itself. Barring that, and if you're still convinced...
2. Think about your position on site
If you have a permanent parking place scoped out, consider wind loading and see if your trailer can be out of direct wind (in the lee of a nearby building, below a hill, downwind of a stand of trees). If you have someone familiar with the land, ask them about snowfall, snowdrifts, if there's a side that is particularly exposed, etc. Consider how you will position the trailer with respect to this. Have you found a spot to put stakes down yet? Alt, you could also look to find an *indoor* place to store your trailer in (room in a prefab metal building or pole barn), and live inside the camper inside the storage. Still going to need to add to insulation.
2. AK Winterize your Roo.
Think about how to attach/build additional insulation to the exterior. Maybe a kind of bracket system, maybe building an external 'house' shell right up against the sides of the trailer, allowing for access by cutting panels and chimney/heat outflow from the hot water heater and the furnace. I think you mentioned 2" dimensionally stable foam, maybe double it up, overlapping seams, glue it together and/or strap it with 1x3/firring strips, even plywood. Carry this insulation down to the ground and make a 'basement' below your trailer. this can be cold storage, but you'll also need to keep your plumbing. underbelly and tankage controlled. You'll also want more than just the factory heat pads - those are simply concentrated at the output areas. -30 will freeze your tankage without batting an eye. Materials and systems start to work very differently in the extreme cold, plastics and adhesives in particular. Can also add insulation to the interior, in particular the bed ends (which you won't be using). Don't forget the windows - these are huge losses - you can add heavy drapes, insulated plastic window covering, etc. Remember that your cabinets don't get conditioned air if they are closed.
You will likely need to heat tape + insulate the entire length of your waste pipes, make sure to get your gate valves. One freezes at -30 and it's not going to open up easily. Consider your water source, as well. City water to the trailer is going to need to be heated till it gets
Note that supply costs up in AK are expensive (including lumber and insulation), and costs for some materials can be 30-50% higher than in the lower 48. You may elect to purchase some of it down here, and trailer it up with you (considering weight implications). Or shop your materials remotely NOW (see what they cost and if they are even available where you're headed vs what you have access too now, or at least, closer to AK - like, purchase in ) and if you want to use your trailer to cart some. (you may be able to take the tent off at least one, if nor both, ends of your trailer, and stack foam on end inside the trailer on both ends in place of the tents AND mattresses (considering that you will be turtling). If you'll be up there in the warm months, you MAY want one tent end and a mattress to use it. Think about heat loss out the top, too.
2b. AK Winterize your truck
This means a block heater at the very least, winter oil, etc. Prep with carrying some extra fuel and deicer. Go through EVERYTHING (from antifreeze to wiper blades), you want your truck ready for the trip and ready to live in AK. Make sure to do the same to the running gear of your trailer, too - brakes, bearings, lights, etc.
3. Keep your trailer light
I would NOT add unnecessary weight to your trailer. Weight gives the false appearance of 'smoothing' a rough road, but comes at a cost by putting a lot more stress on the suspension. Trailer also becomes more susceptible to sway and breakaway control (eg, the heavier your trailer is in comparison to your tow vehicle, the less dominance the TV has have over it. Rigs fishtail forward when a tow vehicle stops faster than a trailer can - the trailer can't slow as quickly, and the only path for it to spend that extra energy is to exchange places with the TV. Worse when the trailer weight increases above the TV). Bring a modest amount of water and only the gear and supplies you'll need to get there. Recall you'll need RV tools and enough to be self sufficient out there on the roads.
Just what I could think off the top of my head. There's a buncha links out there that might point at other ideas, eg:
https://gopowersolar.com/winter-rv-camping-tips-tricks
https://www.fulltimefamilies.com/how-to-insulate-a-camper-for-winter/
https://rvlifestyle.com/how-to-insulate-a-camper-for-winter-use/
Wild adventure ahead of you, buddy. Best of luck.
Hope this helps, I could be - and often am - wrong.
