Hard to tell how this all behaves because the internal resistance of these lipo packs is super low and I guess the original pack couldn’t hold more than 11V for a long time.
Check this eneloop discharge graph to get a feeling for the voltage under discharge conditions
Of course a bigger D cell will be better, maybe a D cell will behave like three parallel AA so we check the 3A discharge graph of the AA eneloops….
This would give around 1.2V and eneloops are well known for the high voltage under load.
I have an ongoing projekt of a light which had 6V Leadacid battery in it, I already bought a 12V 55W bulb and I have a 3S lipo which I want to use in it. I will check how far I am with it later, maybe I can measure the difference between 12V and 11V….