Ultimately, I settled on Tide Clean & Gentle powder. Last weekend, I picked up a box of it from Fred Meyer (my local Kroger affiliate) for only $17. Today, I put it to the test.
I loaded my dirty work clothes, along with some hoodies with oil stains, into the washer. I then poured a scoop of powder (up to line 1) into the detergent drawer. I added in some OxiClean as well for good measure. Finally, I turned off SmartDispense (where the All liquid is typically used) and started a normal cycle with hot water on the "heavy" soil setting. So far, all the powder has fully dissolved with a low amount of suds.
I'll report back once these clothes are fully washed and dried.