Unfortunately you're not going to find an existing tool that handle this type of file out of the box (I even tried it in the not-yet-publicly-available BS Content Studio and it just crashed).
You'd need to manually (or if you have many models, write a program or VrmlPad macro to automate it) get rid of the PROTOs, the 4 Cortona-only nodes (IntegerSequencer, TransformSensor, HTMLText, Panel) and remove the vrmlscript Script nodes before converter tools could handle it.
Only then you will be able to convert to X3D (or other formats), then you'd still need to write javascript for reproducing the type of interactions you had in the Cortona version.
Basically, your only choices are:
write your own converter
get someone to write it for you
wait until Cortona adds a X3DOM export option
(or use another tool than RapidAuthor)
You mentioned that you cleaned up the file enough that it works in Contact so you could try opening it in BS Studio, but you'd still end up having to redo the animations because its X3DOM support is very minimal.