I'd make a template of the plate in 3/4" (or 1/2") MDF the same size as the plate, by tracing around the plate, cutting out the majority of the material with a scrollsaw or jig saw, trimming closer with a router and then sanding to size with an OSS. You can use the plate to see when the template is the correct size, as the plate will fit smoothly within the template hole. When doing this, any bumps in the template will transfer to your final project, so to it carefully.
In my case, the lift and router are very heavy, so I plan to make a 1/2" lip to support the router & plate. If your router has adjustable plates on the bottom for inner-hole size (mine does and 1/2" works), check the range of lip sizes it will handle.
To make the through-hole, I plan to use a 1-1/2" guide bushing with a 1/2" bit, using a series of ever-deeper cuts. With the bushing against the template, it will cut a through-hole that is 1/2" undersized.
Next I will switch to a short top-bearing bit (1/2" cutter diameter xs 1/2" cutter length x 1/2" bearing diameter) in my plunge router and make a series of cuts until I "sneak up" on the depth that makes the plate flush or very slightly recessed.
Finally, I'll use the plate leveling screws to make final adjustments. My table will be from MDF, so I'll "finish" the cut edges with a coat of shellac to reduce wood moisture fluctuations as humidity changes.
You would need to look at the instructions that came with your plate to see if they have specific recommendations, such as lip width and may need to modify your bit / bushing combination.
If your plate will not accept a 1-1/2" bushing, a 1-3/16" bushing with a 1/4" bit would still give you 11/32" of lip. That is mighty close to the 3/8" lip that I've heard a number of folks here recommend.
In order for this to work the radius on the plate must be larger than that of the bit.
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