What ended up fixing my issue was full-screening both programs on the same monitor, then going into OBS and manually resizing both window captures to be the same dimensions. Since my monitor is 1920x1028, I went into the window capture for both my art program and spud tablet, hit Transform>Edit Transformation>then changed the size on each program to 1920x1028.
Once they're both the same size, put both window captures into a folder, then select the folder to resize both captures at once and arrange them where you want them on my stream layout. There's still a teeny tiny bit of de-sync, but it doesn't bother me that much since the custom art I made covers the de-sync.