I have a 2013 Precedent that's 48 volts and I also run the off-grid part of my home on a large 48v lithium pack.
100 amps constant is enough if your cart isn't modified, you live on flat ground, and you don't drive hard... Beyond that, if you have larger tires, drive up hills, carry extra people, or do anything else that requires more load on the batteries, then you really need a 150 amp constant discharge at a minimum.
You will also want to install larger cables to feed the motor and controller.
I have one hill I regularly climb, its about 1/2 mile long and steep enough that my cart slows significantly. I currently run six 8 volt flooded lead acid cells because they came with the cart and are in good shape.
The batteries you see being made for golf carts are mostly the bare minimum.. probably designed for old folks in Florida who drive around their neighborhood socializing. For people who work their carts harder, they are not really enough and I see problems with them tripping out.
The lithium equivalent to the standard lead acid cells is about 3.6 to 4 kWh of capacity, which assumes a lead acid DOD of 50%.
Basically, a 100 amp hour lithium will be about the same as the stock batteries and allow you to clip the knees at the top and bottom of the discharge curves..
That said, the capacity of the battery is only part of the equation. As you have learned, that battery needs to be able to deliver a constant amount of juice without destroying itself.
If you are upgrading your controller for more torque and speed, you should rig for a 200amp discharge.
Right now is a horrible time to be buying lithium batteries.. The demand is high and the availability is low.. Most of what is on the market are Chinese cells and I won't risk my investment. I'd rather have EV cells.