I use 2200mah NMH AA's. Just put AA holders instead of the 'D's'. AA's are a couple bucks a pop. I charge them about every 5 hours of use to keep the volts up there close to 1.4v each as possible. I also run higher voltage (45-50v Lipo4). Love that Quickie!
Rechargeable Batteries in series don't like filament/ resistive loads. One of the batteries can get reversed biased and that causes bad things to happen.
The garden solar lights you buy drive a LED. The LED stops drawing current before the batteries get badly damaged.
Question for you guys: Before finding the above mentioned batteries I was considering paralleling a pair of D batteries or alternatively several lithium AA batteries just so I could go a little longer between battery changes. Would that be a problem with the filament circuit?