Hi Wheels.
I've no answers for you here as I'm trying to get my head around managing BG levels during intensive training too.
I, equally, have no idea as I've only been diagnosed for about 4 months or so. I was actually on here today browsing on the subject of workout/training related BG dips so came across your post.
I can manage my BG fine during low-aerobic activity but find my numbers drop significantly when at high intensities, be that longer high intensity such as steep hill climbs on the bike, or shorter but intense activities, like higher-rep sets of deadlifts or squats.
I avoid sports energy supplements, other than sugar free electrolytes during long exercise, as I'm wary of the impact of them and have found that planning what I eat around my planned training activity has been, so far, the best - if not perfect - way for me. If I know I'm training when I get home at 6pm, you'll find me having a bowl of oat, seed and berry porridge at half-past four, for example, and a good balanced meal will already be prepared so I can start refuelling right away.
Your non-gym day BG seems like quite a range though. 3.5 is right into hypo territory (unless you use a different measurement scale than I do - I'm sure there will be more than one). You eat healthily as you say but are you balancing your carbs and sugars on those days when you exercise less?
Might the intense exercise BG dips, be a function of your medication and your exercise regime? That one might be worth talking to your DM Team about. I'm just guessing; other than a week on meds when first diagnosed, I'm diet and exercise only at the moment, so I am entirely unqualified to do anything else.
Really interested to hear how you get on with this. Learnings might be shareable.