I’ve had a similar experience — both with having to pick gapes at sub-optimal times (curse you, weather!) as well as having that rough white residue on my crush equipment.
The residue, which resembles a thicker than normal layer of hard water scale, comes from the grapes themselves. From what I understand, it’s simply an organic acid/mineral complex very similar to the common tartrate crystals (solidified tartaric acid) often that can collect in the bottom of bottles or barrels. I find that it comes off very easily when cleaned with TSP, “Peroxycarb” (a commercial brand of powdered sodium percarbonate) or a similar basic cleaning solution.
Always be careful when cleaning stainless steel because you don’t want to scratch, score, or pit it. These scratches, if you aren’t careful, are ideal environments for microbial spoilage organisms to hide and wreak havoc on your wine. I try to use as little force and abrasion as necessary to remove the scale; stick with gentle sponges or brushes with plastic bristles (no metal!) only. As always, when using a basic cleaning agent (pH greater than 7.0) to clean, follow by an acidic (pH less than 7.0) rinsing solution like 1⁄2 oz. (14 g) citric acid diluted in 2 gallons (8 L) of water and finally by a clean water rinse. That should do it!