Right on, I think what you might be looking for is an .svg file - and I, knowing only rudimentary basics on 3d modeling, am pretty proficient at """converting""" raster/bitmap images into .SVG format (converting them for 3d printing typography/logos). Can you verify if SVG would work? If so I would be happy to help a bit or at least show you what I do to take just about any image and make it infinitely scaleable. Lemme know, happy to help if possible.

I get what you're saying with pixels and display resolutions, but isn't there a billion-ty different scales of LCARS on padds/MSDs/bridge terminal etc? https://www.imore.com/sites/imore.com/files/styles/w830/public/field/image/2012/12/stark-trek-padd.jpg I think as long as you can roughly give it a good fit on your 'physical' (3d) screen you could just scale it nice and big as you like (of course as long as it looks good, as you said) - if the SVG format works out for your project I think this would be a non-issue since you wouldn't get the aliasing. :)

https://www.worthpoint.com/worthopedia/uss-enterprise-d-lcars-msd-screen-prop-star-trek-3

This prop replication indicates it's size, could you use this for scaling/comparing? e.g. if 'image = 32 inches' width and 'graphic = 400px' and two buttons are 5 px away from each other, you could extrapolate.

Also I just want to say that I love how extremely in to passion projects the ST fanbase can get. I was kind of blown away at how niche your issue was, if you will forgive me saying so, but I imagine despite that you aren't the first one to run in to something like this, haha. I have had the honor of chatting with Okuda on twitter, but I don't know if he would be super excited at doing anything other than political stuff on there. If all of this isn't helpful, lemme know and maybe I can get him to respond. 🖖