Do you do your own work?

If you pay a bike shop $100 an hour to poke around on a 40 year old bike, the bills can start racking up quickly. If you do your own work, then by all means, go ahead and fix it up.

If the bike hasn't been ridden for 20 years, I'd give it a good cleaning, pull the hubs and bottom bracket apart, and repack the bearings. Probably the headset too.

I believe all Shimano (old) chainrings were 130 BCD, so you can get a 38T chainring if you wish, but it may not be necessary. It depends on your riding style. Are you spinning up hills, or standing? As others have mentioned, you can easily change the cluster.

You can often fit a 6 or 7 speed freewheel on an older bike where a 5 one was standard. It may involve moving some spacers from the left side of the hub to the right, and re-dishing the rear wheel slightly. You don't need a lot of clearance near the chainstays. There is a lot of MTB stuff available with 7 speed freewheel clusters, so they are available, with big gears for hills.

DNP Epoch is the only one that is currently manufacturing a freewheel with 11T for the smallest cog (downhill, fast on level, etc), with a couple of fairly lax upper range options. The freewheel has a bit more backspacing than I like, but it is worth considering. Your bike may have something like a 13T-23T cluster, so you'd snag a few extra gears on both ends (but skipping at least one tooth between every gear).

I kind of gave up on sewups a while ago and moved over to Clinchers, and am not looking back. There are many flat resistant tires available now, and I'd strongly encourage you to consider them. The sewups are apparently also improving, so you could use them if you wish.

Also consider getting clipless pedals. I've settled on SPD pedals/shoes as they are the most comfortable for a little casual walking, but there would be arguments for different types too.

Alaska? Is that summer riding or winter riding?

You can get studded tires down to about 30mm which may fit on your bike. There was a recent discussion about Wolvehammer boots for cold climate cycling.