If your V8 one sticks in first sometimes it is on it's way out, you may get 100 miles or 20,000 miles, but something isn't working as it should.... re-reading Ashcroft's site they site it as being the governor needing cleaning or replacing, though it sounds like you probably already know this.... an oil and filter change and governor clean may well fix it, but you are taking a chance.
The 300TDi box is definitely different with change points more suited to the diesels power band, the V8 would work as is, but not be ideal. The torque converter for the diesel box is smaller than the V8 IIRC too.