Long story short I ordered Tioga Powerband to try on the rear but ended up putting in up front first (it's a front specific tire but I think it'll work on the rear quite well). Originally, I had a generic Kenda 20x1.5. The Powerband, 20x1.85, is much taller adding about .5" to diameter and (only) 5mm wider (43mm on 17.5c rim). At 345g +25g liner it's still lighter than Kenda and about 165grams lighter than the Big Apple (and $15 cheaper).
The result so far has been nothing but positive. Powerband rides so much smoother with a lot less vibrations at the handlebar, it seems to be rolling easier, and it definitively offers more grip while braking - especially in wet conditions. Bottom line, no more rattle while riding over sidewalk or over small holes in the road.
Puncture resistance remains unknown, but with added panaracer kevlar felt liner, wider footprint and low psi I hope it'll perform. If punctures do happen, with 190g advantage, I'll try using thorn resistant tube as a plan B
Here's the link to tires profile: Powerband