Re-reading your OP, you indicate that this is mostly on unfamiliar stuff, and that with stuff you know, people say you have good time. You're doing the best possible thing by noticing your issue. That's a requirement to solving problems, clearly identifying the problem.
A little trick I use on myself...if I clearly state my desired outcome, my best case scenario, out loud to myself....that has to happen before I can achieve it. Writing it down is even better because it's like you are giving your brain instructions you want carried out. Very powerful tool. Whatever thoughts are in your mind will tend to manifest themselves, (for better or worse) if you just keep thinking in those terms. So think good thoughts!
Transposing that to your case, I'm pretty sure that what you want to be able to do is keep steady time on new material, steady time everywhere. Me too! So what's happening? Are nerves responsible? An uncomfortable mental space you're in with new material? Seems highly likely. Maybe just cut yourself a break and don't try to be so good at first. I think you need to trick yourself into going to a different, more productive headspace when confronted with unfamiliar material. Dumb it down if you need to at first. It's OK. You are completely capable of keeping good time if you relax and get out of your own way. What you are doing now isn't working for you, according to you. Maybe try closing your eyes with new stuff, that always helps me. It frees up a lot of brainpower. (not having to process complex visual images) It helps me to feel things easier, no distractions.
You've clearly identified your issue, rushing on unfamiliar material. You've even made it public. IMO, once you can state the issue out loud, your unconscious mind works on correcting it, if that is your desire.
It's been almost 2 weeks since you first posted. Have you noticed any progress in that certain area?