OK, not that you've posted a picture and mentioned the new chain, I can ell you what changed causing the problem.
The new chain has bulged outer plates making it a bit wider than chains with flat outer plates, which your original chain probably had.
I'm not as big a bear on riding crossed over as others here, and often do it (both ways) when the situation makes it convenient, such as approaching a steep changing climb from a flat or shallow grade. Here I prefer shifting the front, and tiding small/small, so I'm ready for progressive downshifts as I climb.
Odds are that if you switch back to a flat plate 8s chain the rubbing will be eliminated.
__________________
FB
Chain-L site
An ounce of diagnosis is worth a pound of cure.
Just because I'm tired of arguing, doesn't mean you're right.
“One accurate measurement is worth a thousand expert opinions” - Adm Grace Murray Hopper - USN
WARNING, I'm from New York. Thin skinned people should maintain safe distance.