Since you are using a 4x5 camera with a 47mm lens, you probably do not use any swings and tilts. This might be a way to solve the problem digitally.
The first step is to make a "mask frame" using the same (I assume colour) film that you normally shoot with. Using B&W for this mask frame might be acceptable but you may need to adjust the contrast slightly in photoshop if your real image is in colour. If you are using different lenses, say a 90mm with swings and tilts, it might be necessary to always take a mask reference frame. If the lens such as the 47mm has different light fall-off at different apertures, you might need to create a few mask frames at different apertures.
Take a single frame of a uniformly lit large white card - possibly a 3 foot by 4 foot white foam core board. Put the card reasonable close to the lens to ensure that it is quite out of focus to remove any of the white board surface texture - probably set the lens for infinity focus or at least your real subject's normal working distance. Expose should be for reflected light middle grey (i.e. believe your reflected light meter - however an incident light meter should work just as well
) I think the 18% metering is correct in that it is in the centre of your film's characteristic curve and therefore is not affected by the shape of the top or bottom of the H&D curve.
After you scan this mask frame image, you can now use it as a gradient to darken the centre or lighten the edges.
The "mask frame" should be converted to B&W. If there is any surface texture from the white board still showing, use the minimal radius Gaussian blur that will remove this unwanted detail. It (hopefully) will not cause any noticeable change to the gradient of the mask frame. If the mask frame white target was not perfectly uniformly light, the minor corrections to the mask can be made in photoshop.
Load your "real image" as the background layer.
Load your "B&W mask frame" above the background.
Since the mask frame was exposed for 18% grey, it will be overall too dark. Therefore adjust the layer opacity to some small value (i.e. 5% or what ever seems reasonable)
Depending upon which blend mode you use (such as Subtract, Soft light, Lighten, etc), you need to invert the mask frame layer or not.
(( I tested this process "in principle" in Photoshop ... it seems to work ... basically, it is just a variation of vignetting. I am assuming that the process will work in the real world
))