Yes, everything you say suggests too much basal being a long term problem. I find that basal will magnify discrepancies in boluses: too much basal, and I will seem to get more action from a bolus, too little basal, and a bolus will often not seem to work as well. What is more the previous doc's approach sounded brittle and slap dash. So yes, your comments make sense to me.
It can be upsetting and frustrating to have such systemic long term issues being caused by such fixable things, another member here was (half) jokingly offering a hockey stick to someone to hit their doctor with, I'd be passing it along to you for your old doctor. But - rest assured you are not alone in going through that kind of thing and now you can look forward to things being better now you are on a better track.
Speaking of which, it's good you are systematically reducing your dose. Get your new team/doctor to agree that the best dose is the one that works and therefore establish that you are capable of finding and changing it yourself. it's good you are doing a fasting test in the morning. You should consider doing further basal testing, that's the best and in some ways only way you are going to get information about
:
1. what dose you should be using, what time of day to take it
2. What daily background fluctuations in your system are occuring that give you "trouble" spots such as recurring hypos.
In other words, you will somewhat be able to profile your basal requirements (which may be flat or may have fluctuations). Either way, knowledge is power and could allow you to know what is going on and adjust insulin, food, lifestyle, accordingly. Here's a good read for basal testing for MDI.
Basal Testing for MDI - Diabetes Daily Forum
If you continue to find there are frustrating limitations to your insulin therapy you should look into getting a pump if possible. They can afford a huge amount of tweaking and control over basal (and bolus) compared to long acting insulin.