“Transparent” overdrive recommendations

I’ve decided to get a more “transparent” overdrive. I use an SD-1 but have come to understand the difference between that pedal’s sound and a BD-2, and now I want a BD-2 or something like it. Before I pull the trigger, I wanted to know what the best options are. There’s so much out there comparing dozens of overdrive pedals and want some help cutting through the noise. I’m getting lost trying to compare the BD-2 to the Fulltone OCD to the Keeley Super Phat Mod to the JHS Morning Glory to a Wampler Belle, etc. etc. Not able to drop the cash for a Klon or a King of Tone, but would love to hear your thoughts on what BD-2-like pedals you like and why.

Edit: Thanks for so many suggestions!