Jamesb, what happens if you only move the ElkAccts.mdb file? Even better, copy it first, so there's a copy in both locations. Then use the File/Open Database to open the new copy in My Documents.
I'm guessing that RP tries to open the operators database first and dies if it doesn't find it.
Of course, if you want to live dangerously, you can always move all the files, then just update their locations in the registry. Search for elkaccts and you'll locate the configuration in:
HKEY_CURRENT_USER\Software\VB and VBA Program Settings\ElkRP\Settings
What I did is move the 3 .mdbs Control, ElkAccts and Ops, then update the 3 associated registry entries. The first time I opened RP it complained, then I shut it down and moved the SOps.mdw over too. It seems to need to live with Ops.mdb. RP appears to work fine now.
As always when messing around like this, backup *everything* first. YMMV and I'm not liable for anything!