You cannot disable the L1P/L1D on the c671x. I expect your problem is one of cache coherence. Are you performing manual cache operations before branching to an application? So in particular, in your secondary bootloader I suggest that you perform a writeback-invalidate on all address ranges that you touched immediately before branching to the tertiary bootloader. Similarly, I suggest performing a writeback-invalidate on all addresses you touch/load immediately before branching to the application.
After a cold power-up, only L1P and L1D are enabled, i.e. L2 is disabled. The L1 is a read allocate cache so as long as you're just doing reads from external memory and then writes into L2, you shouldn't actually be caching anything. I think the issue comes due to having so many layers of bootloaders. For example, if you have a local variable of some sort in the L2 for the secondary bootloader, then that variable would be cached in L1D. Then when you're in your secondary bootloader if you go to write instructions into that same location, because it's already allocated the instructions will "land" in the data cache instead of the actual memory! Performing the writeback-invalidate will "push" anything that might be cached back to the physical memory and make sure that nothing stays allocated in the cache. That way you can "start fresh" for the next piece of code.
If that's not it please provide more details on your cache handling. In particular be sure to specify whether you're doing writebacks, invalidates, writeback-invalidates, whether they're local or global operations, and the precise timing of the operations relative to other key functions like branching to the app, etc. I hope this helps.
By the way, in addition to the "cache" guide there's also one called the "two level internal memory reference guide". That one also contains important details related to cache operation. In my mind they are tightly related (i.e. seems like they could have been one document), though that's not how we did it! So be sure to consult that one too (SPRU609B).