The place names are large enough to read comfortably when I select a 256x256 texture but when displayed in a square window which is almost the full width of the screen ( portrait mode, so 1080 pixels in 'HD' ), it's only using about a quarter of the screen resolution.

If I step up the output texture size to 512x512, sure enough the resolution improves but as was said, the same view effectively 'zooms out'. When zoom is corrected to frame the same area as before, the place names are much smaller and not as easy to read.

Because of this, unless there's a good solution to fix the issue, I'll just be displaying my maps on a 256x256 texture.
not ideal but what can you do?

My point was that less of the map is visible.  Yes, it's larger, but there's also less of it which does not suit my needs.

#1 is not possible.  The size in the scene directly correlates to how large it appears in the real world as a hologram.

#2 gives me this:

Note that the actual area covered by the map is much closer in.  Milwaukee is no longer visible on the initial zoom level.  My attempt to reduce marker size was also not successful.

#3 is not available as we are not using Mapbox Studio.

You have three ways:
1. Increase size (in scene), and reduce the size of the markers.
2. Use the small value of Width / Height (pixels) and reduce the size of the markers.
3. Increase the font size of the labels. Currently, you can do this only using Mapbox Studio Classic.

I tried reducing the texture size, but that also had the effect of displaying a smaller area and increasing the marker size (which isn't necessary).

When it first starts loading map data, it looks like this, and quite readable:

But a few seconds later, it looks like this:
(Note that the zoom level is unchanged, any apparent difference in size has to do with where the device was in relation to the map: I was having to take screenshots with one hand while interacting with the hololens with the other, all while being unable to look at my laptop to insure that I was taking the screenshot at the right time).

Marker size is about right, maybe a little small, but the map is an apparent 15 feet away (and about six feet wide).  It is filling the displayable area on the hololens device, though.  But quadrupling the size of everything (that is, changing the Online Maps width/height from 1024 to 256, so that the available area is 4 time smaller) makes the font readable, but the markers become huge and map-dominating.  This is undesirable.

Note also that in the second screenshot I included some of our UI text for comparison. Pixelated, yes, but still readable.