1. Both of the dumps I tried are BIN/CUE
2. File size of Dump 1: 557 MB (584,135,664 bytes); File size of Dump 2: 557 MB (584,135,664 bytes)
3. CUE sheets: http://www.bwass.org/bucket/Lunar2SCDCUEs.zip (To RHDN staff, please note that these are just CUEs and not BINs. You cannot play the game with just these)
These are the most two common dumps on the internet. I can't say in specifics where they're from, but they are from popular sites. Dump 2 is a Darkwater dump that needs to be uncompressed as an ECM file. Apparently, the Darkwater dumps are supposed to be the most accurate out there; "It matches the Darkwater database to be a perfect 1:1 replica of the retail disc," according to the place I got it from.
(I hope this is informing enough without being too precise.)
This is exactly what I needed, thank you! Your two CUE sheets line up with each other. They indicate a total size of 248357 sectors, whereas my original copy of the game is 248507 sectors. One of the copies of the game I've seen circulating online aligns with my copy, while the other is a 248357-sector disc like yours is. I'm unclear whether that indicates that there are two Working Designs builds, or if one of the two rips is misaligned sector-wise. Two builds is very unlikely though, because 100% of the files between the two rips match, as does the bootsector.
How are you patching the game, by the way? Are you applying the .xdelta3 file directly to the .bin file, or are you doing something else? What tool are you using, and what command if it's a commandline tool?
I had been using ISO/WAV/CUE. Would my CUE still be of use?
My fixed patch specifically targets the BIN from a BIN/CUE or the IMG from an IMG/CCD/CUE set; it won't work with the ISO from an ISO/WAV or ISO/MP3 set like Supper's original one did.
I had a question. Would it be possible to transfer the higher-quality soundtrack found in the Saturn version of Eternal Blue Complete over to the PSX version? I attempted it myself a year or so ago but didn't get very far due to my lack of coding knowledge.
I don't think this is feasible for the PlayStation version... but I'm going to be translating the Saturn version when I'm done with SSS and Supper and I are done with MSL.

It will probably be at least a year, maybe more, so please be patient - but there will eventually be good news. And I agree with you that the Saturn music is much better!