I've hit a similar issue in my game, it's a puzzle solver where visibility of the whole puzzle is useful and the level designer has assumed that it's a 1920x1080 screen with 64x64 blocks. For the other resolutions, typically lower spec PCs, the choices as mentioned above:
1. Draw to an off-screen texture at 1920x1080 resolution and then scale on screen (maybe with the text overlays rendered at the native resolution for simplicity)
2. Draw directly to the scaled ratio
The advantage of #1 is that it's the simplest (I do this for my UWP version so users can resize the window without killing my puzzle aspect). The disadvantage is that you're burning compute cycles to do so. Whether this is important depends on the rest of the load on your GPU. For me, it appears to be irrelevant though.
#2 allows a much greater flexibility, but does require greater resources (i.e. those for 32x32, those for 64x64 etc.) Along with probably slightly more complicated rendering logic.
Reading your post more though, you talk about a strategy game - and hence I'm assuming that being able to see as much of the battle field as you like is important. I'd almost argue that users would expect to be able to zoom in / out regardless of screen resolution, so I'd be inclined to go for option #2. You could do as @Zakwayda points out and use standard mip-maps and if you're allowing zooming to be done dynamically, I'd go down this route. Otherwise, you could do this in the resource generation stage of your pipeline, so you only ever load in a single resource set rather than loading multiple and subsequently deciding which texture set to use per frame.
Also, for the aspect ratio, for my game (puzzle in a space station), if a user resizes to a weird ratio, I just add black bars on the appropriate side. Again, for a strategy game, I'd be inclined to let them play with whatever ratio they have.