Something to consider:
The timing chains on these rides are under constant pressure (with the engine on or off), which results in the timing chain stretching (especially on a car that has sat,).
When the chain stretches, idle, acceleration, basically everything about how the ride runs is affected. And most of the "indicators" will make you swear you'll "need a new carb".
So, have you checked the timing man? That is where I'd start.