Alan:
The governor in the BN1 can still be incorporated with a single relay circuit. Just put the governor switch in series with the dash switch. Both switches would need to be closed to activate the relay and fire the solenoid and either switch opening would downshift.
I think the real purpose of the relays is to prevent the overdrive from disengaging without blipping the throttle which momentarily opens the throttle switch. The throttle switch should play no role in engaging the OD if it is set up properly. However, I have seen throttle switches rigged to serve as sort of a kick-down switch, to downshift if you give the car enough throttle. That is not the way it is supposed to work, according to the shop manual for either the BN1 or BN2.
I think connecting the OD solenoid directly to a 12V source controlled by any switches you want would work fine, though you would not get the throttle switch disengage feature of the relay system. The solenoid does draw a huge current but only for a few milliseconds, once it activates the it just takes a few amps to hold it in. I don't think it would damage wires or switch contacts as long as they are reasonably sized.
If you bypass all the bells and whistles of the relay system, beware of the following: if you stop your Healey with the OD engaged and back up, you can seriously damage the OD. This is not likely to happen, but I have seen it occur, just keep that in mind.
Good luck!
Bill.