Downwash gradient is the relative change in the downwash field (behind the wing, specifically as experienced by the tailplane) with change to wing AoA.
It's a VERY significant factor in assessing the longitudinal stability of a configuration - as a rule of thumb, for every one degree change in angle of attack at the wing, there's about half a degree of downwash change.
What that means is that the wing 'straightens' out the disturbance before it gets to the tail, and so SIGNIFICANTLY reduces the effectiveness of the tail in countering any disturbances.
In fact, it depends on the relative position of wing and tail - if one were to have a tail located directly next to the wing, the downwash gradient would be very powerful - taken to extreme, one can conceive of the tail being so close to the wing, and the flow being so 'straightened' by the wing, that the tail would not actually experience any AoA change at all. Consider T/E flaps - whatever my AoA is at the leading edge, the flow angles at the flaps are very much invariant, because the wing defines the flow, not the AoA.
A similar phenomon occurs on canard-deltas, especially 'close coupled' designs like Eurofighter, where the downwash field from the canard has a marked effect on the AoA and efficiency of the wing unless great care is taken.
And I'm sorry, but I see no way for this to contribute to the longitudinal stability of an aircraft, except in very special circumstances that aircraft do not encounter routinely. (near-stalled surfaces)
I'm trying to conceive if it has an effect on speed stability, but I can't visualise how that might work, either.
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an aircraft in level flight cannot hold a trimmed attitude without a degree of longitudinal dihedral.
Sure it can. Hawk has an all-moving tail. Hawk has a wing incidence of +1 deg. I
guarantee I can find a flight condition where the stab angle is also +1 degree - in fact, I'll be able to find a whole family of speeds/weights/cgs where the tail angle to trim is +1. The tail range goes either side of +1 on Hawk, if it couldn't ever trim at +1 we wouldn't have bothered with the tail having the travel it does.