Edit: New version in post #66
Ok, at least for my PS2 model v10 PAL [ger] i found a method to run the original OSDSYS from uLaunchElf after booting from "free McBoot"
This does need a "compatible" OSDSYS in your PS2 rom having the "feature" i use, so if it works for you - great - if it doesn't work there's nothing i can do... this uses something already present, so no patching done at all - just standard ELF loading. If the "feature" is not present you will probably get a reboot into uLaunchElf because OSDSYS will then look for updates, invoking free McBoot, ...
Attention: Do not have a disc in the drive while launching... as it is starting the unmodified, unpatched, built-in rom:OSDSYS that one will then immediately try to launch the disc instead of going to the browser. Strangely we will then get the same drive problems as in uLaunchElf. If your drive is empty and you insert the original game disc after OSDSYS has launched then the original game will run fine.
Best place to put is into the boot folder and then link it to some button in uLaunchElf instead of MISC/PS2Browser.
As I said before: No guarantee at all that this works for you, but for my PS2 it does.