The jump from 0.8 to 2.3 was more worrying than the latest jump. NHS guidance states that greater than 2.9 needs investigation, but that is very poor guidance. It would be better if it talked about rate of increase, but that would need two tests a few months apart and that is beyond the capabilities of patient management systems.
I think you should have been monitored annually after the second test. However I think you have been lucky, you could so easily have been in the group I referred to in my previous post who end up with significant cancer.
With your PSA history I would say a biopsy is a good idea. Even if the biopsy comes back positive you shouldn't be worried, if you have cancer it is probably a very slow one. You may be able to postpone treatment for a decade or so. I don't think any man should rush in to suffering the side effects of treatment earlier than they have to.