In fact, considering that they are only achieving a 5 year life (ish?) from these devices, it beats me why they bothered with a rechargeable battery at all, and didn't just use a non-rechargeable Lithium battery. Ho, hum. 
Kevin
Would a cheap lithium have the power to sound the PS? Also, I guess its fair to say the alarm has to be able to recover from going off occasionally...
9 times out of 10 the vehicle battery will be powering it. They are also quite efficient in terms of db sound per Watt of electrical power. I guess it comes down to cost. NiCd pack being cheaper. 
Kevin
Would be an interesting experiment to replace with a lithium pack as suggested, and time the sounder before the pack discharges (Ear defenders anyone?). As a lot of the newer (& cheaper than when these were designed) batteries can hold a charge for a considerable time, could that be considered a long term solution?
We change or smoke detector batteries on an annual basis, so why not our PS's? Admittedly it's not easy due to construction of the PS, but I'm sure that a "how to" mod that could be written to make it easier each year?
Even basic soldering skills could facilitate an external battery pack if more power was required?
Again, insurance issues, but certainly better than no PS at all
Obviously a "proper" solution is preferable, and you guys have certainly spent time & effort, and have reached a lot of important conclusions, but if there is no answer, it's expensive, or can't be found maybe this could be considered?