You shouldn't get chain rub half way down the cassette on an 11 speed set up. I only notice mine doing it on small (chainring)/small (11T on cassette)
It's curious that you say this didn't happen with the previous SRAM Red chain until recently and you say that the new chain has now been reduced to 114 links - the same length as the original.
It's also a bit of a coincidence that you can buy SRAM chains in 2 lengths - 114 links and 120 links
https://www.sram.com/en/sram/models/cn-1170-a1
I may be wide of the mark but maybe the original chain was fitted as supplied with all 114 links and never shortened (because whoever fitted it couldn't be bothered or didn't know any better) to the optimum length for your bike and you were just lucky or didn't notice an issue until the original chain got older.
If it was me I'd still shorten the new chain further. Or if you've still got the old chain shorten that by a couple of links or so and give it a try. When and if you're happy with the way it's running count the number of links you've got and replicate on the new chain.