DC Forklift high current power supply
Given the limited amount of run time that you need, I'd seriously look at using automobile (car) batteries.  They will need to be decently-beefy batteries and should all be identical, purchased at the same time and hopefully from the same manufacturing lot.

Having identical batteries makes charging them easier.  The real concern is that some cells are lower capacity than the rest and those cells will charge and discharge differently from the rest.

You will get decent run-time if you keep the batteries charging while you are using the unit.  Instead of trying to build a huge power supply that has to run everything, use the batteries as an accumulator.

You will need 3- 12V batteries of about 100 AH capacity to get the 36 Vdc rating of the existing battery.  If you have the budget, double the number of batteries (3 sets in series of 2- batteries in parallel).`

You will also need to reduce the amount of current that the existing charger supplies - it is sized for the existing battery and most likely can deliver enough current to damage the smaller batteries that you are going to use.