I'm not sure if anything I can say will provide any novelty for the OP but it's worth a shot I guess
Are all the games you burn sizable enough to fit on CD containers?
CD-ROM will fit on burnable CD's that have max capacity of 1GB
DVD-ROM can fit on CD container if game is below 1GB stock, or after removing dummy files
If you can't fit DVD-ROM on CD, then you burn it to a DVD5 which has max capacity of 4.7GB
There is also DVD9 (Dual-layer, 8.5GB) but I have never burned any of these
https://en.wikipedia.org/wiki/PlayStation_2_technical_specifications#Optical_disc_drive
Also, this Wikipedia entry referring to "Later models starting with SCPH-500xx being
DVD+RW &
DVD-RW compatible.
I have a Slim PS2 (SCPH-75001) with modified memcard using [FreeMcBoot v1.966 Build 2019-04-13]
All ISOs are patched before I burn them using FDVDB ESR Patcher Gui v0.4
After an ISO is patched, I burn it at the suggested speed using ImgBurn (which is 2x or 4x I think, been awhile...)
The DVD that I use is 4.7GB Verbatim DVD+R [RW]
I do not have an example for CD's because I don't think I have any CD burns laying around the house
I could never get CD-R/DVD-R to load, even when using ESR Gui to patch the ISOs before burning them.
But with DVD+R, I've always had the best of luck and the game usually loads (sometimes slow) and plays well.
Since your console is 30K series, I don't think it works with RW capable discs which means you are probably looking for discs that don't have that function or perhaps that part doesn't matter and the RW could just be ignored but I'm not sure...
Other users will tell you that -R discs can work (it's just a personal view of mine, could never get them to work)