I found a fix for the texture aliasing. Using EQ-Zip I exported and re-imported the textures in the lakeofillomen_obj.s3d file and that fixes it since EQ-Zip will, by default, add mipmaps to the DDS files when it imports. It looks sooo much better now.
Using EQ-Zip (instead of S3DSpy) should also make Psycher's upscaling process easier since it automatically exports the DDS files to PNG with a PNG extension and automatically imports the PNGs to a DDS format with a BMP extension. It also supports flipping the images to deal with the issue with the chr.s3d files by using some menu buttons.
Link to EQ-Zip
So the steps for upscaling could be reduced to the following:
Export textures from s3d file using EZ-Zip
Upscale textures in Topaz Gigapixel AI
Import textures back into s3d file using EZ-Zip