Need Some Help

Don't use a tractor battery. Yes, they are larger and have more capacity, but are "flooded" which means they are full of liquid acid that could spill if you dump your scooter. You will never get enough lead batteries on that scooter to give you full throttle for 2 hours. That would be about 2 kilowatt hours of enery. Since you can't drain a battery to 0, the pack would have to be bigger than 2 KWh. If you need speed and 40 miles of range, this is not the right scooter to start with.

If you just want to have some fun in your neighborhood, you could replace your bad batteries with 3 new 12V 10Ah Sealed Lead Acid ones that would fit exactly like stock. You could still use your stock charger, in fact, you can use your stock 36V charger on any 36V pack.

If you want a little more "pep", you could try adding a fourth battery (48V) and maybe a 48V controller. Your existing motor should handle the additional voltage without problem. You would see a noticeable improvement in speed (are you REALLY getting 20 MPH now?), and, depending on what controller you are using, increased acceleration as well. The only downside to 48V is that you would either need to buy a 48V charger, or rewire your scooter to be able to charge from one (or more) 12V car chargers.

There aren't a lot of Stealth scooters on this forum. I hope I've helped you some.

Just because a battery is physically larger doesn't mean it has more voltage. That is whether a motor would be fried (your word) depends on the voltage. If the voltage is too high the motor will "fry".

The "crapping out" you describe is typical of the battery having lost its capacity. Batteries lose capacity if they're too old (a.k.a. have had too many charge cycles) or if they've been mistreated. Common mistreatments are to over-discharge the battery pack, or to leave it partially discharged for a long time, or to simply leave it sitting for a long time without charging. The last one is because batteries self-discharge over time and a partially discharged battery gets damage over time.

The SS 1000 doesn't have a lot of room on it for a larger battery pack. Tractor batteries are rather large, eh? Since the scooter runs on 36 volts you would need three batteries to equal 36 volts. How would you fit three tractor batteries onto the scooter and even if you did it's unlikely to be able to move afterward.

If you really want the longer range it will mean using a completely different battery chemistry that has higher energy density. For example lithium-ion.