The flashing process normally includes a verification that the BIOS was written successfully, so given that the recovery process appears to finish as expected the flash chip wouldn't be my first suspect.
Now, since the recovery works we can assume that the critical parts of the boot process are working, that is basic chipset initialization, CMOS/RTC (in the Dallas chip), floppy (handled by the SMC I/O chip) and some other stuff. Let's think about what is not needed on the recovery process: since no video can be displayed in the recovery process due to limited ROM space, and no peripherals other than the floppy drive are used, maybe initializing the PCI to ISA bridge is not necessary during recovery.
Now, my knowledge about this is very limited, but it could point to the 82378 bridge chip where you had to repair the legs. Maybe there's still something wrong with that one? Short, unsoldered legs, or something like that. Given the condition it was in when you got the board that chip must have been hit pretty bad.
Just my speculation, of course it would be much more useful to know what the 'EE' POST code means...