Mark,
With the little i know from what you have posted, baking would be the last thing i would do (if at all i do it!). Sulphuric acid has a boiling point of about 290 centigrade, and with a little bit of moisture around when baking you will only end up eating up the metal parts in the detector.
You might want to check the safety procedures of your company. Most safety departments in a company wont be happy if you play around with radioactive sources. Which model/make ECD are you using? If it is something like Thermo GC's, you can actually remove atleast the counter electrode and clean it with some solvent. If it is something like Agilent's uECD, i am not quite sure how it can be handled.
Good luck fixing the ECD!
Suresh Seethapathy