/u/burnt-store-studio - So, I reached out to a drummer from one of my old bands I hadn't talked to in years - I figured he'd at least get a little joy out of me being clueless on this.
What we're looking for is actually pretty common, but it just doesn't look obvious at first - At least, it did not for me.
This is what he directed me to here. I expected a smooth, pre-built gap for this base to slide into, but it's more like my experience helping set up drums in general: A lot of loosening things and then tightening them around other things. If you look at the head of that unit, you'll see the gap where the base for this unit goes in. If it doesn't make immediate sense to you, let me know and I'll take some photos.
I had one of these drum stands: https://www.amazon.com/gp/product/B00HX9F1OQ/ref=ppx_yo_dt_b_search_asin_image?ie=UTF8&psc=1
That uses a mounting bracket for electronic gear: https://www.amazon.com/Gibraltar-SC-EMMP-Electronic-Module-Mounting/dp/B00HX9F1N2/ref=pd_bxgy_img_2/141-6729595-9196722?_encoding=UTF8&pd_rd_i=B00HX9F1N2&pd_rd_r=e8c0d9f9-ff33-47b1-b077-f1d7897f2737&pd_rd_w=kvbEJ&pd_rd_wg=dWIt5&...
And I used that to attach a nice piece of shelving board, 18" x 11". But really, at this point you don't necessarily need music gear; could look for a smaller profile standing desk.