If you’re not set on using a chrome control plate then making one is a possibility.
I’ve made a couple of plates using 2mm aluminium which once cut and shaped I then epoxied on some 1.5mm maple veneer. The maple was stained black (full thickness) first and then once glued on was sanded and tidied up then coated with multiple coats of CA glue or poly.
Old work in progress pic, top plate was coated with poly and bottom is CA glue with a beveled edge to show the Al.
Cutting the slot accurately was the hardest part, so it should be a lot easier without one. You could maybe try brushed or even etched aluminium using 3mm pieces if you wanted.
You could possibly even use some pickguard acrylic as a tester to design a plate, but it would likely flex too much just using two screws to hold it. Some 1mm Al on the back probably solve that.
Or, be really slick, and do a rear control cavity so you don’t have to worry about a control plate at all. You can get a jack with longer thread for mounting from a rear cavity too.