From what you say, it is probably worth replacing the shift components, particularly the stopper arm and spring which are known to give trouble. It is very difficult to tell whether the spring is weak or not as no specification for it are given to test against. None of these parts are expensive and are easy to replace (especially as you've already got the clutch out). It is worth giving this a go first, before splitting the motor. Always best to try one thing at a time, starting with the cheapest and easiest!

We have seen several instances where failed stopper arm components have caused two gears to select at the same time resulting in transmission lock-up and serious engine damage.

Just out of interest, does it jump out of third into another gear, or into a "false neutral"?

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