If your app is in control (and knows when the ANALYZE is going to happen) then perhaps the best approach would be to try and control the use of prepared statement handles?
If you defer loading your Class::DBI modules until after the bulk load has finished (or are you using Class::DBI for the bulk load?) then it seems that might work around the problem.
One way to defer the load of some modules until run-time is to wrap the 'use' declaration in a string-eval, e.g. eval "use My::Class::DBI::Module;". Another is to use:
both of these approaches pull in the module at run-time and so can be used to move the Class::DBI loading until after your ANALYZE, if you perform them in a function rather than at top-level.
There's probably a better way, though.