I have just 'been there' on this - and I've now gotten some excellent results with LR and AI GigaPixel. Earlier UpRes'ing using LR+PS Preserve Details 2.0 produced some horrible files and when I redid them using the AI GPX workflow the results were hugely improved. It was difficult to see the impact on screen, but very obvious when comparing the full size prints. AI GPX was much better.
Here is what I did after getting the really artifacted prints
I when back to my original raw files (OLY OMD-EM1 Mk II) are re-processed them a bit more subtly. I applied some overall noise reduction, but then specific noise reduction in smooth areas like sky. I set the sharpening back to about 13% (e.g. pretty much off) and was careful I did not overdue Clarity or Texture. All this to ensure I wasn't creating artifacts in this first phase that would be amplified by AI GPX. I added the vibrance and lighting as needed.
I exported the file at the cropped resolution without any resizing to a ProPhoto TIF at 16bits; no compression. So, straight TIF file to a temp location. About 39MB.
I dragged this into AI GPX and set the output File Format to a 16-bit TIF, no-compression, maintained the ProPhoto color space. As I am printing to HP, which is native 300, I was upsizing to a 12000x12000 pixel file (from something originating at roughly 3000px)-so I guess that's roughly 400%. To set these settings, I had to turn on Convert File Format to (YES).
AI GPX took 10+ minutes to run on a 2013 MacPro with dual AMD FirePro D500 graphics cards - e.g. I used the GPU not the CPU option.
This created an output file in the same folder perhaps 892MB in size. I imported that back into LR in the same folder as my original. No issues with the import. I then turned on the sharpening (52%, Radius 1.8 and with Masking about 42). I choose these parameters viewing the image at 1:1 on my monitor and holding down the alt key while adjusting the sliders to see the impact in B&W. A higher radius is required when you have this many pixels.
I printed this directly from LR's print module on 44" paper, at 40"; output print sharpening Matte-Medium. Earlier on I considered Relative vs Perceptual and since I was very much in gamut on the original, I stayed with Relative.