I don't think I have a good understanding of the lift curve slope
As much as I normally abstain from using potential flow theory to explain things, for this purpose it is actually useful.
In potential flow theory, lift can be calculated as the linear superposition of a contribution from camber and one from angle of attack. While the camber-related part of lift is constant, the angle-of-attack related part varies linearly with this parameter. Think of a wing as a vane which re-directs the flow of air slightly downwards: The higher the angle of attack, the more downward velocity is imparted on the air. Looking at the impulse change caused by this redirection we find a force, the resulting aerodynamic force. This can be split into a component orthogonal to the original direction of flow, called lift, and a component parallel to it, called drag.
As long as flow stays attached to the surface of the wing, the streamlines and flow patterns look very similar to potential flow, except for a small layer around the surface, called the boundary layer. Once separation sets in, the linear relation between lift and AoA breaks down. The variation of lift over the full range of AoA is shown in this answer.
I get that high AR wings will stall before low AR wings but what makes that true?
Since the pressure difference between the lower and upper side of a wing can equalize at the tip, local lift drops the closer you move to the tip. This tip effect is larger in low aspect ratio wings simply because more of the wing area is close to one tip. This means not only that a low aspect ratio wing needs more AoA to create the same lift as a high aspect ratio wing, but also that the pressure gradients over it are more shallow at the same AoA. Therefore, separation needs more AoA to develop on a low aspect ratio wing and it will reach a higher AoA before stall.
Still, the tip effect will reduce the total amount of lift the wing is capable to develop. If you look at the local lift distribution of a rectangular wing over span, an increase in aspect ratio will make it look fuller. The decrease in lift at the tips will affect a relatively smaller part of the wing while the part away from the tip will show an almost constant lift over span. In other words: The wing is working harder, so the stall speed of an airplane with a high aspect ratio wing will be lower than that of a comparable airplane with a low aspect ratio wing. Only the vortex developing on highly swept leading edges will reverse that trend.
From the comments:
how exactly do leading edge vortices affect stall speed of higher and lower AR wings?
The vortex only forms at high sweep, which prohibits a high aspect ratio. By adding a rotational speed component to the air on the upper side of the wing, the pressure there drops further, adding more lift and lowering stall speed. Of course you want this low pressure to work on as much area as possible, so the inner chord of a wing with voretx lift should be high. Which invariably leads one to a delta wing. And deltas only come with a low aspect ratio.
Typical stall angle of attack of a high aspect ratio wing: 10° - 12°
Typical stall angle of attack of a low aspect ratio wing: 15° - 18°
Typical stall angle of attack of a delta wing with vortex lift: 25° - 30°