Thanks to everyone who replied. I appreciate it.

I ended up going with blackmateria's solution:

s/([\x80-\xFF])/'&#'.ord($1).';'/eg

Since it kept the scope of the substitutions neatly to just the things I wanted to replace (as opposed to tommyw's followup using [:print:], which—as I understand it from page 80 of the owl book, at least—would have performed replacements on tabs and other non-space-character whitespace as well).

Thanks again to all y'all!