Learning to listen to my body and stop over-exercise I have the tendency to push myself too much, resulting in exhaustion and 4+ days of required rest and more than a week before I can train normally again. Two weeks ago, I went on a 35 mile ride which includes several steep hills (7-15%) and I just wore myself out too much. I just can't keep cool and cycle slowly- a reason why I have never ridden more than 40mi. I don't know when I am doing too much. Or rather, I ignore my HR meter and think "just this bit and then I will slow down".

In the wake of that, I discovered spinning as a great way to constantly monitor my HR and not push myself too much. I thought I could maybe use spinning as a way to learn to listen to my body?

Every summer, I partake in a TT race. I would love to finally earn some silverware. The TT is short (13.3mi) and I think it doesn't take much for me to improve. But I just can't improve, because I always over-do it. Is there something that I can do? I have dropped most of my cycle workouts for spinning in the past month because I recover much better. But I want to get back on the road, especially with the weather improving.

I also do weight-lifting, which is easier to do because if it's too heavy, it's too heavy. But with cycling, I can always tap into a reserve.

Clear question: What excercises are there (aside from resorting to spinning) to stop over-exercise during a bike ride? How can I improve my awareness?
Learning to listen to your body equates to developing discipline in your training.  Changing the type of exercise can help you give specific muscle groups rest but you can still exercising without the discipline to meter your effort and therefore not actually rest.

My suggestion is to write out your exercise plan and journal how you do.  The aim of the plan is to allot time to hammer your body with space to let your body recover.  That also means you choose your exercises and routes appropriately - no hills on easy days.  Keep track of what you do, be diligent to stick to what you write down.  If something isn't working, change your written plan, but follow your plan.  DISCLAIMER: Consult a doctor regarding your efforts, 4 days of forced recovery means you aren't recovering and you risk severe injury and burnout.

Discipline is an additional "muscle" that you will need to exercise, strengthen and push to its limit. The harder you work on your discipline the more consistent you will ride, the better you will recover and the more you'll know about what your body can handle.  

Developing a plan and learning to meter your effort will pay dividends for you TT as well.  No amount of strength will help you in your race if you blow your energy within 1 mile and struggle the last 12.3 miles.  

Best of luck.