so just run a small wire as long as you can get it

I did that when I was keen to listen to shortband, it got blown down in a gale and I found that for medium wave, the length of co-ax up to the loft worked just as well and cut out interference generated in the house rather better, so I never put it up again.
However, I think that your point on getting a 50's/60's receiver, from when AM was important, is a very good one.