Try disassembling your top tension assembly and setting it to a looser baseline. You might not be able to get low enough with the way it's setup now.
I don't trust automatic lower tensioners though for featherweight fabrics, they just don't work from my experience. So try to adjust it by hand. If the lower tension is ever too tight (pulling the top thread flat along the bottom of the fabric), it's obviously no adjusting automatically.
FWIW, I have to recalibrate the tension on all of my machines to handle 20 and 30d fabrics, and I'm not surprised that the machines you tried didn't work. However, I will say, that no offense to Ray, but the horizontal bobbin concern is unfounded. My 500A handles sil with ease.
$2,000 machine means nothing, almost no standard machines are setup for low-tension sewing, and only a few (like the Juki DDL-8700) common industrials are, although your thread could still be too thick.