Congratulations on getting up the gym.
Hypos, damn annoying, we try to o something positive and it all seems to go awry.
A good cardio workout has the same affect on me as it appears to have on you.
Personally I never change my basal dose ( lantus for me ).
I've read your post and one thing I would say is........ you say you start a workout at 8.0, which is good but that's soon going to drop with intense exercise. You take 2 / 3 Glucotabs.
Imagine if you was going on along car journey, a few hundred miles let's say.
2/3 Glucotabs would be like putting enough petrol in your car to get you to the next petrol station.
Better to put enough petrol in for the journey and not leave it until the last moment.
In your situation, through a bit of trial and error I would look to take some long lasting carbs on board prior to exercise.
I find malt loaf good also a banana and peanut butter. Eat maybe an hour before your workout. You want the carbs hitting your system as you exercise.
I think you're doing everything right, just try different things and you'll get it right.
Good luck, keep exercising, because no matter what, it is a great benefit.
Hope this helps.