Well, welcome to OCC!
The XT1-LT42E is a new completely electronic Cub Cadet. Unfortunately you aren't the only person to have issues with this machine.
For the battery, Cub states that the machine will run for up to 2 acres or 1.5 hours on a full charge. How much do you think your battery is lasting per charge?
And for the speed control, take a look at the speed control pedal and it's linkage. Perhaps there's a sort of dampening shock absorber that isn't connected? If there isn't one, perhaps you could add one to it.
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'70 107 with k301 engine swap
'71 106 with 38" deck
'70 147
R with factory replacement k321, 42" deck
'61 Original with 38" timed deck
'63 70 "pinkie"
1863 with 54" deck
'46 Farmall H, '50 Farmall Cub
105 x2 (parts)