Although a rare event if the diff., is faulty it can result in one drive-shaft getting more power than the other. Plus the steering will be a bit more heavy turning corners.
One other possibility is a duff engine mount especially the top one.
Wot 'e said.
Sounds like acceleration is changing the game, and the harder the torque output (highest in the lower gears) the higher the effect.
As a thought, if the diff is driving one shaft more than the other, would that show when doing circles left compared with circles right, at low speed, and also when under power.
But we're basing the investigation on the information that you've had the suspension checked, and nothing is apparently wrong. This sort of pulling sounds like bushes/trackrod/track-rod ends, and that should be easily detected.
Remember that checking with the wheels on the ground is differnet from checking with the wheels hanging from the suspension, as the bushes are at the end of their travel (and out of their normal wear area) when the suspension is hanging. (I had a drop-link that hid behind this issue; it was easy to find once it was on a four-post ramp)
If you have a suspect engine mount, you can try loading it (using the clutch for a hill start, say) and should not get much engine movement. If the bonnet is open, you could see if an upper mount is gone; the lower ones are harder to see!