I have the 2011 LR4 with the 20's/5 spoke and I went through same (painful) thing trying to find the semi-aggressive tires that won't rub.
So... Here is what I did:
Falken Wildpeak All Terrain trail tire 255/50/r20: https://www.falkentire.com/tires/light-truck-suv-cuv-tires/wildpeak/t-trail-tire
These Falkens ride smooth and quiet on dry pavement and have the snow rating so no chains needed usually in our ocassional California snow. I am in So. Cal, so I only need snow tires about 12 days per year when we go snowboarding/skiing.
Alternative...
I came very close on pulling the trigger and buying a set of 19" like you have and roughing the look up by going super aggressive off road-ish with tires, then switching for winter, but we just don't get enough off-road in this family to justify switching back and forth, so the Falkens on the 20s are a good blend for me.
Good luck! Let's see if we can ride these LR4s to 200k.
