Thanks for the info.
Not an easy one to answer, but will do my best.
Forgive me for stating a few obvious things below ( and all are from my personal point of view, what I have studied and personal experience and experimentation in the past ).
1. As you would know diazepam is very long acting.
2. At low doses it works as an Anxiolytic medication (+-2mg)
3. At slightly higher doses it works as an Anxiolytic Sedative medication (+- 5mg)
4. At higher doses it works as an Anxiolytic Sedative and Hypnotic medication (+- 10mg)
Those dosage strengths are an estimate from my experiences, and obviously I am chuckling to myself by typing 2mg, I mean that would not have had any effect on me, however it is a good guide for people who have no tolerance to benzos/gabba meds.
OK, now to answer the question "How to counteract sleepiness from benzos without caffeine or stims?" - your heading of this thread.
The 100% way would be to not take any sedatives.
But that isn't helping you and something a pompous doctor would say.
The only thing that helped me back in the day when I was taking them was once the initial benefit/calmness/relief had kicked in and the "tiredness" or "emptiness" feelings started, I would smoke a small joint.
It worked. Not for hours, but it did take away the "sluggishness" and gave me a "recharge" so to speak.
If you are taking 25mg or 35mg (which I think I might have seen in a previous post of yours, but could have been for the purpose of sleeping or something else that was a necessity at the time for you), there isn't much you can do to "counteract sleepiness", as this is the whole purpose of taking a medication at that dose and then wanting to "undo" it. IMO it is a pointless task and just creates more frustration and ultimately is detrimental to one's mind and body.
To sum up this lengthy attempt at a suggestion to avoid "sleepiness", then if you are taking a higher dose in order to rest - accept your decision and rest.
If you are looking to take something for a calming and fruitful few hours, then take a smaller dose ( anything higher then 5mg is not a small dose IMO ).
If this smallish dose starts making you sleepy after the initial release of the benzo and you need a small "pep me up", then smoke a small joint or a few drags/hits/puffs even.
If you don't smoke cannabis for any reason the only way I can think of would be to take the lowest dose of diazepam possible.
I hope this helps in some way and I hope you find the peace and inspiration you deserve and please don't take my post as a form of "instruction", I am just sharing what I know.