Inverse panorama

Use a single resolution target and pan your camera.

Remember that the goal is to obtain an image formed through different ray geometries of glass at the edge of the lens. You don't necessarily need to image through the glass of the center of the lens while doing so. To that end, you could accomplish your task of measuring sharpness in the corner using a panoramic photography rig. The difference is that, this time, instead of making multiple pictures to capture more than the FOV you will use multiple pictures to capture less. Some of the most advanced optical meteorology equipment in the world utilizes a single target and extremely accurate lens positioning systems.

There is plenty of information on creating a DIY pano rig here and on the web but for this test even a carefully measured lazy susan or turntable would work. To set the rig up you will need to mount that camera in your panorama rig with rotation around the nodal point as normal but also such that it is not horizontal. Instead you need to mount it at the angle corresponding to a bisecting angle of your sensor (that is the angle between the long side of the rectangle and a line going from corner to corner. The formula for that angle is angle=ATAN(height/width) Where height and width are either pixel counts or aspect ratios.

Once your camera is mounted at an angle, panning your panorama rig will cause the target to move from corner to corner. You are now ready to capture. Start with the target in the center of the sensor as a baseline. Next, move halfway to the corner and measure again, finish with the corner then repeat on the other side. If your lens contains an aspheric element you may wish to make more than five measurements so that you can look for third or fifth order trends in resolving power.

I'm not sure what your current measure of resolving power is but I will point out that SFR is a powerful metric for understanding lens performance. SFRMat used to be freeware and you can probably find a copy floating around in the web. the current version free trial allows 40 measurements. SFR or MTF tools can also be gotten from MITRE but I cannot vouch for them.

Freelensing could enhance your measurement accuracy further. Assuming you can effectively mask any stray light between the camera and disconnected lens, panning the lens while keeping the image in the center of the sensor has the advantage of not experiencing resolution loss to the sensor. This is an especially big concern with wide angle lenses due to exceeding the critical angle of the microlenses

Focus point is a matter of personal preference. Spherical aberration will make the focal plane for the edge of the lens different in the corner than it is in the center. You must therefore decide if you want to focus for the center and include spherical defocus in your measurements or focus each measurement to isolate that variable.

There are a few other ways to accomplish this task but I don't want to complicate this answer.

As a side note, Imatest produces a "pre-warped" resolution target for use with fisheye lenses. If you do want a target that can measure an entire lens in one go, they may be able to help. Expect to spend $1-4k US to get started though.