Yes - the reason you have that +2.5V reference is that it is there to provide a signal ground; it makes the 0V look like -2.5V, the +2.5V ref look like 0V, and the +5V supply look like +2.5V.
On the spec sheet for the OPA2335 it even boasts of its "Single supply" operation, right at the top of the page. Most opamps can run this way, but it's an indication that was what the designer intended for this circuit.
Yeah I noticed that alright and I figured it was at least a good part of the reason I've been having problems. I'll try the setup you've recommended here anyway and I'll let you know how I get on.
Thanks a million for all your help.