Try leaning to each side, front, back etc. and see if any position makes it better or worse.
Or just move it a bit so the plunger travels a bit more.
Could also be a chafed wire between the seat switch & attachment swith.
OTOH, possibly fuel related.
Is this the first time you mowed this year? maybe a bit of water in the bottom of the carb bowl.
When you engage the blades, governor opens to bring the engine back to speed and it "gulps" more fuel.
I'm just trying to get you to isolate between electrical and "other".
With the number, I can look at the proper schematic to see if it might have an OPR involved in the kill circuit.
There must be close to 100 different LT 1000 model#'s.