Recovery? recent "make world" rendered system unusable (64 bit change)

I've been running 5.1-CURRENT for a while and a couple nights ago did
a "make world".  After a couple hours building, my system was
unusable.  Critical binaries like "rm", "ls", "mtree", "sh" failed,
reporting "Exec format error".  I can't login, not even single user.
I can no longer even boot single user.

I've hosed my system and am looking for a way to recover without
having to reinstall everything and overwrite critical data and system
config files.  Naturally, I only discovered the note in UPDATING after
I trashed my system -- in fact, I read it from the "OK" boot prompt
with its "more".  Doh!

  20031112: The statfs structure has been updated with 64-bit fields
  to allow accurate reporting of multi-terabyte filesystem sizes. You
  should build world, then build and boot the new kernel BEFORE doing
  a `installworld' as the new kernel will know about binaries using
  the old statfs structure, but an old kernel will not know about the
  new system calls that support the new statfs structure. [...]
  Running an old kernel after a `make world' will cause programs such
  as `df' that do a statfs system call to fail with a bad system
  call. [...]  DO NOT make installworld after the buildworld w/o
  building and installing a new kernel FIRST.  You will be unable to
  build a new kernel otherwise on a system with new binaries and an
  old kernel.

I'm looking for recommendations on how to recover, hopefully without
trashing my critical system files like /etc/passwd.  Ideally, I guess
I'd like a way to replace all the broken binaries and any related
libraries without overwriting other files.   

If I do a floppy-based install and then select Custom/Expert than
request a minimal install, I presume it will install a small set of
binaries but also overwrite /etc/passwd, /etc/ssh/* and so on.  Is
there a way to have it just update binaries and libraries?

If I have to, I could add another disk to this box.  Then I could do a
floppy install of 5.x on to that new disk.  Then I could boot it, and
mount the old disk's partitions. Then install the new install's
binaries on the old partitions.  Or perhaps I could do a make
buildworld, kernel, installworld the proper way, using the old disk's
partitions as the target.

Or could I -- somehow -- push a 64-bit-aware kernel onto this box so
that the newly "broken" binaries will work again? How?  Again, I've
got no shell access any more so everything's gonna have to be done
from floppy or maybe CD if I can borrow a burner. Naturally, this is
my net boot server for my diskless clients so I can't go that route
either. :-(

Any other suggestions?  Thanks.