Is there any way to force the lens to stay open at a wider aperture?
Your question implies a misconception: as you focus closer and the reported aperture is decreasing, the physical aperture is not actually closing down. The camera/lens is reporting the effective aperture.
The effective aperture is given by:
where E is the effective aperture, N is the aperture setting ƒ-number, and M is the magnification of the lens at a particular focus distance.
The magnification M is the ratio of the image distance di (the distance from rear principal plane of the lens) to the object distance do (the distance from the front principal plane of the lens to the subject in focus): M = di / do.
Practically, you usually don't know the image distance. You usually don't know the subject distance accurately (especially at close focusing distances), but you can estimate it fairly closely. If you rewrite the magnification ratio in terms of focal length ƒ and subject distance using the thin lens equation, you get an equivalent expression:
So from those equations, you can see that the effective aperture is equal to the real aperture (the focal length of the lens divided by the entrance pupil diameter) only when the lens is focused at infinity. At infinity focus (or even just very large subject distances, such that do ≫ ƒ), the magnification is basically zero, so the effective aperture E equals N.
But when do is not significantly larger than ƒ, the magnification M becomes appreciable enough to significantly impact the effective aperture.
As a matter of interest, but not directly pertaining to your question, let's compute where the front principal plane is for your lens. Using the reported effective aperture E = 5, we find from the effective aperture equation your magnification is about M = 0.79.
Solving the magnification equation for do, I get a subject focus distance of about 409 mm. But your table reports a focusing distance of 525 mm. How can this be? Firstly, both the reported aperture of ƒ/5 and the actual set aperture of ƒ/2.8 are probably not highly accurate numbers, so some error most likely propagated there.
However, even if we could account for the inaccuracies in the ƒ-numbers, the subject distance do would still be less than your reported working distance, simply by the very nature of your Sigma 180mm being a telephoto lens: telephoto lenses move the principal planes out in front of the lens. Thus, the optical subject focus distance is less than the actual subject-to-front-of-lens distance for a telephoto lens.
For more on telephoto lenses, see: