Since I have grooves that touch edges of the acrylic sheet, the export treats those as if they are the actual edge. To solve, I placed cubes and blocks (in red below) along the real edge in Tinker. In Estl, I chose my 1/8" bit and am cutting along the inside edge of those blocks using the engrave tool, manual left side. Select all the important points then hit Enter. The edge of this engraving touches the groove. The groove itself is pocketed to its appropriate depth using the engraving tool, same procedure. Select the points of the groove then hit Enter. I chose manual paths and left side so it cuts to the correct side of the line.
An important step is the red blocks are moved 0.01mm away from the left and right edges of the white rectangle. You can perhaps see it on the top screenshot. This is important because if they perfectly abut, the TinkerCAD export treats red and white as all one unit, so there are no lines in EstlCAM to draw a shape around.
It’s a hack, but it works.
TinkerCAD looks like this. Between the red and white areas there is a grey shaded area which is a half depth groove.
EstlCAM looks like this. The slightly darker line is the groove.
Thank you @SupraGuy for helping me get my groove on