Is it possible to "over-train" in samatha meditation?

I would recommend a relaxation exercise before beginning any meditation e.g. you focus your attention first on the feet and gradually work up the body consciously relaxing each part in turn.

If you are willing to read, I think you will enjoy Alan Wallace's "The Attention Revolution: Unlocking the Power of the Focused Mind". This book is only about satama, about the levels of focus, the benefits, the hindrances and some pitfalls.

My current plan is to keep to that gradual build. (...) But does the same thing apply for "mental" exercise -- i.e. for Buddhist samatha meditation of the kind I describe?

For sure. If you go to 1 hour right away you will probably just get yourself tired. And also, I think it is much better to meditate for 20 minutes every day than one hour once a week.

Should I "hold back" even though I'm keen to do more?

I think if you are willing to do more, go ahead. But like physical exercises, you should improve the quality of the practice (i.e. focus and stillness), instead of just increasing the duration.

Is it possible in any way to "injure" oneself by over-training when it comes to meditation.

Yes, but only if you have some severe mental illness, or if you do a long recluse retreat.

These are just some quick answers. But I strongly recommend you to read Wallace's book, because it is much more extensive, detailed and instructive.

I aim to sit for an hour in the early morning and an hour in the evening. I find samatha meditation more difficult and sometimes I break the sit before the hour is completed. When I do noting, I experience impatience less and therefore I am more likely to complete the whole hour. If impatience does arise, it can simply be noted as impatience, impatience, impatience, until it passes away. Often I begin with samatha for say 10 minutes and then when I feel that my concentration is strong, I shift to vipassana. I sit in the classical meditation position with my legs folded under. I find that I can hold myself totally still for an hour or more in this position, though in the colder months my knees get abit achy by the end of the sit. I can't sit in any lotus variation for very long. I found that I began to get better results once I was able to sit for longer periods of say 40 minutes to 1 hour.

First, physically, you're probably always going to cause some pain by sitting in a strict posture unless you've been doing it since you were young. So if a person had just started meditation and did so with a great deal of zeal, I could see them causing some pain and stress in the body by doing too much at once. They might even cause some permanent damage if, in their zeal to do it right, they won't sit in anything other than full lotus, even when they're causing pain.

The bigger issue though is that, mentally, there's the danger of getting burned out. Thanissaro mentioned in one of his talks he had friends who would go out into retreat alone for long periods and the problem they would run into is making no progress. Weeks and weeks of no progress in their meditation. It must be tough to become a monk, have one goal, do nothing but practice toward that goal and end up making no progress.

I think it's universal: your practice will have ups and downs. There are times where the mind becomes more and more focused, it lets go of all discursive thought, the precepts become easier to follow, and then there are times when it seems you're sliding backwards.

All in all, the real danger, if there is any, of overtraining is this mental burn out, because when you sink a huge amount of time and energy into something, you want to see short-term progress.

As to whether it would be better to do less sitting than more, I'm not sure. Are you the kind of person who takes on new projects easily and then gives up easily when you encounter difficulty? I suppose the more short-term oriented a person is, the more I'd recommend they just take things slow and steady so that they don't run into a patch of doldrums, get frustrated and give it all up entirely.