The answer is "no" - a rewrite rule won't work.
According to RFC 3986 the '\' character is not permitted in URIs; Cisco updated the URI parser in 5.2.2 to be fully (or, at least, closer to fully) compliant with this RFC (bug CSCud39381).
To revert to non-strict URI parsing, we had to create a parameter map:
parameter-map type http NONSTRICT-PARSING
parsing non-strict
and apply this to the appropriate class in the interface policy map:
policy-map multi-match global
class BROKEN-APPLICATION-CLASS
loadbalance policy BROKEN-APPLICATION-POLICY
appl-parameter http advanced-options NONSTRICT-PARSING-PM