I worked out the doubling time about the same as you have. So it will take 3 year to get to 1, another 3 to get to 10, and another 3 to get to 100. As Barry says these are hardly precise and it may accelerate, but in 10 years you will have a PSA of over 100.
I don't think you can say what PSA figure is the one which determines whether you live or die. If you had a PSA of 1000 but it was all happily sitting in the prostate bed theoretically you don't have a problem.
In reality I think if you ignore this you will probably live another 10 years and then things will be really messy. If you have a good QoL now, maybe you should think about Active Surveillance; you might manage five years before things look scary, then get treated, have a bit of a miserable two years in your late 60s rather than your early 60s. And hope whatever treatment you have pushes the next recurrence twenty years down the line.
Some people say if it needs doing I may as well get it done now, but my philosophy is that, in the next five years you could get run over by a bus, have a stroke, a heart attack or a whole host of other bad things. So whilst life is good you may as well enjoy it and not spend two years on HT, but as the risk of PC increases and as your quality of life inevitably declines due to aging, and assuming you haven't bypassed the need for treatment by dying in the meantime, then yes go for treatment at the last possible moment before the cancer becomes incurable (I'd like to think that might be five years time).
Of course you and your oncologist need to make the decision. If I were the onco I would be pushing for ASAP, let's get this sorted, but if I were the patient for the reasons above I would be looking to hold off as long as possible.