How well do repeated runs of the same material agree?

How do you manage trimming, sag or leakage from the perimeter of any cone & plate, or parallel plate tool pair? Might such edge effects be proportionally larger for smaller tools?

I do not know you material that well, I have no idea about the typical shear rates, viscosity, solvent etc. There are quite a few things that can go wrong. Evaporation, sagging of particles (which you can easily check with Stokes law), air bubbles, viscous heating (i.e. you dissipate too much energy in your sample and then the temperature increases, especially at high shear rate), flow instability, inertia effects causing material being thrown out of your plate-plate or cone plate, inertia effects of your set-up, i.e. have you waited long enough to reach steady state. Further what is also important whether you measure stress controlled or strain controlled. I assume you measure strain controlled. Most rheometers nowadays are stress controlled, which makes it easier to measure yield stress. When your set-up is stress controlled I would also measure stress controlled, which makes it also easier to prevent that you exceed the maximum torque.

Further in a cone-plate the shear rate is constant in your sample, which is not the case for a plate-plate. When you do not know your sample it is better to use cone-plate.

One of first things you must indeed do is to verify whether you measure with each method consistently, i.e. measure several repeats. Please have a look at the book of C.W. Mackosko, Rheology, principles, measurements en applications, VCH, 1994. Good luck !