To get good quality, nothing will beat increasing the resolution and regenerating portions of the image.
That's why having a local installation is so important, since you can't do image to image in civitai.
Tile resample controlnet worked really well in 1.5 at keeping the shape when regenerating in image to image. You could set the denoise at 1 and be fine. But tile resample isn't available with sdxl. You can try other controlnets, but you'll have to set a low denoise.
I could train a 1.5 version of the LoRA so we can use tile resample. I'll have to think about it. I think with bucketing selected I don't have to rescale all of my training set images. But it would be better for the quality to crop the images rather than rescale, and that's quite a lot of work. The set has 700 images I think.
But considering that the style doesn't have a lot of detail, using tile resample isn't excessively useful. A simple image to image at low denoise on an upscaled image is pretty much good enough.