I do use it quite a bit and the remote has a decent size screen which also shows what's on and what's off and also transmits back to the remote verifying that something HAS happened.
It is powerful. I've started my car when it's been WAY out on a walmart parking lot and I was inside when I did it.
I've also done it from inside an elevator and of course, inside the shaft.
From your description, it sounds like this is a relatively high power, intermittent discharge for the batteries. Given that, I am surprised that the alkaline cells outperform the Eneloops. It might be that your remote has a relatively high voltage cut-off, and if that is the case then the PowerGenix cells might help.
You might try the Duracell PowerPix cells. These have the same chemistry as the PowerGenix (zinc-NiOOH), so they operate at the same high voltage, but they are constructed like a conventional alkaline cell. The Duracell PowerPix cells are not rechargeable, but if they last longer than conventional alkaline cells, then it would be a good bet that the PowerGenix cells would also work well for your application.
So to summarize, I would say that you have the following options to improve performance:
Duracell PowerPix (non-rechargeable)
Energizer e2 Lithium (non-rechargeable)
PowerGenix NiZn (rechargeable)
Let us know what you try and how it works.
Cheers,
Battery Guy