Well, let's start that the OD shouldn't engage in reverse other than 3rd or 4th gear in forward. I'm sure that did some damage beyond the broken spring found by the mechanic. How much, hard to say without getting into the box.
Answering your questions, there's not a difference between the differential of the OD versus non-OD cars. There is also no difference in the length of the driveshaft. The OD and non-OD units are the same length, the tailshaft making up the difference on non-OD trans.
In terms of running the car with the OD disengaged, as long as it is not making audible, ominous noises, chances are it is fully disengaged and should operate fine as a 4-speed. Just as a note, my OD was added, my car being a 4-speed from the factory. It quit last year (an electrical issue, but I just don't have time to look into it) and I drive it as a 4-speed with no issues.
What you do next is up to your driving choices and your budget. The OD cannot come out without removing the engine and trans, so a fairly involved job. Then there's what you'll find when you open it up. Finding a decently qualified shop to work on it is another challenge. Fortunately, the OD unit is the same for MG, Jaguar, Austin-Healy and others from the era, so while still a small cross-section of transmission shops, it's expanded a bit by the added marques.
If you have time and are familiar with the OD unit or have a cooperative shop, take it out and open it up.
If it's too far gone, go for a rebuilt from Moss or Victoria British. Victoria British offers the type D OD you have as an outright sale for about $1,000 (part no. 2-1043-R), so the condition of yours doesn't matter.
From Moss, you'd have to upgrade to the later LH type from the 68-up cars. Cost is about $1050 for the OD unit, but that includes a $300 core charge for your old one (which has to be in rebuildable condition), so a net of about $750. You will probably need the later trans mount for this as well.
Check with your local shop on what they would charge to rebuild it. You may find the V-B or Moss prices comparable.
Also, depending on your budget, how you use the car or how original you want to keep it, the alternative to go to an American 5-speed is available as a kit. Moss offers it (part no. 440-075), as do others. The new trans is the same as used in a Mustang, so parts and service are easy and readily available. It also offers the added feature of being able to be removed without taking out the engine, as it is set, like an American car, with the trans bolting to the new bellhouse from the back. This makes for much easier clutch changes down the road as well. Cost is prohibitive at about $4,200 from Moss, but includes trans, bellhouse, shifter & linkage, driveshaft and trans crossmember & mount.
I hope that helps you. Let me know how you make out.
Safety Fast!
Art Isaacs