DKMS isn't the only package that will run into problems, really hand compiling kernel modules will probably hit the same roadblocks.
I think the most appropriate solution is to fix these packages before they're deployed on the cross compiled architectures. It doesn't make sense to have binaries from the native builder on those machines. Those last files should be recompiled for the correct target architecture at the end of the build process after they're used on the machine to cross compile all modules.
DKMS isn't the only package that will run into problems, really hand compiling kernel modules will probably hit the same roadblocks.
I think the most appropriate solution is to fix these packages before they're deployed on the cross compiled architectures. It doesn't make sense to have binaries from the native builder on those machines. Those last files should be recompiled for the correct target architecture at the end of the build process after they're used on the machine to cross compile all modules.