After opening the DR1000 a few times (adding an on/off switch and replacing the mini-USB connector with an type A), i'd say replacing the battery is possible. You'd have to find a (Varta?) battery with roughly the same dimensions though. There was a thread in this forum some time ago discussing this.
I've been looking for some time now for a replacement battery. The original Varta battery (PLF503759 B) was difficult to find. Farnell has a PLF503759, but it seems that that particular model is not manufactured any more. Alternatively you could think about other brands 3.7v lithium-polymer batteries. I found an IPaq battery that looks promising, though it has a higher capacity. I'm tempted to use a higher capacity, but as discussed in that old thread, the hardware (and software?) of the DR1000 could cause trouble there.
Is there anyone out there who has already tried this kind of replacement?