I think I need to replace the headset on my 1989 KHS Montana Summit mountain bike, which uses a 1 inch threaded headset with loose bearings (if memory serves, but they might be caged).

The reason I think I may need to replace it: It works loose after only 200 to 300 miles or so, and yes, it is assembled properly, and the threads are not damaged.

Would it be worth the expense to upgrade to a roller bearing headset as sold by Velo Orange?

The bike is going to be used for everything from around town to long distance self-supported touring both on and off road in all types of weather, including cold, rain, snow, to dust storms and hurricanes when one of the bad weather possibilities hits while I am on the road.

Murphy's Law states in its complete form: "If anything can go wrong, it will; and at the most inopportune time."
And, let us not forget The General's Credo: "Mr. Murphy was an optimist."

If the headset "works loose" and the threads on the steerer are not damaged then the locknut is not being tightened sufficiently against the top race. Replacing the headset won't solve that problem.

If bicycleridr4life is riding off-road, the headset may, indeed, be working loose. This was a constant problem with mountain bikes back in the day and there was a whole cottage industry built around locking headsets that included shaft collars and locking nuts. Here's a couple of examples.

On the other hand, if the current headset has loosened after only a few hundred miles and has done so several times, the cups and races are probably damaged and the headset needs replacement anyway. I'd probably go for the sealed bearing unit over the needle bearings. The sealed bearings are easier to replace if necessary.

or... the cups were never properly seated in the headtube by the, ...er, mechanic... don't ask me how i know this.

This is one of those cases of more data needed. Headsets that mysteriously loosen despite tightening, usually have worn cups and bearings and need to be replaced. Small wear in the crown race can also result in loosening. But the usual case is that there is a tiny bit of play at different fork rotations that will indicate this kind of wear and you're likely to sense that when stopping. So the question is, do you have play in the head set when adjusted properly if you turn the steering left/right and try to rock the fork with front brake applied?

If you don't have play, do you have hints of "indexed" steering when you have the bike in a stand with no additional force on the front steering? If you do, then you probably have to replace the headset.

With older bikes, I've had reasonable success with Tange Passage headsets. They have seals, and use regular balls and are a low as $10 a set and come in 26.4 and 27.0 crown race. I like the low-end Ritchey headset as well which is about $20, but it's a 26.4 crown race only. I don't have a current source for 27.0 Ritchey compatible races so it may only work on older bikes with 26.4 crown race. If you don't know yours, you can remove the crown race and it's sometimes stamped on the underside. Or get some really good calipers.

I've had the same problem on threaded headsets that use aluminum locknuts. Most recently on a Miyata 912. I suspect is has to do with their greater thermal expansion than steel. Regardless, I fixed it by cleaning the threads and using blue locktite.

It's worth a try since you have nothing to lose. Everyone has locktite, right?

If this is the case then it was the assembler at the factory. The headset is original to the bike. I'm pretty sure the bike is out of warranty now, darn it. I suppose it would not hurt too much to ask the dealer who originally sold the bike if they would replace the headset under warranty. They could use a good laugh I suppose.

No "indexed" or gritty steering, play seems to be the same no matter which way the bars are turned.

Chris King Headsets use a Cartridge bearing. They make the bearings too.
so there is no loose relationship, between bearings and their races.

I have a 1" 2 nut, and a 9/8" Gripnut on threaded forks.