I have the same issue after upgrade from 2.1.10 to 2.1.11.
The only thing that I've found now is a very slow Redis lib, it takes up to 99% of whole "Admin Login" action time. Make a note - not Redis service, but Redis php lib.
Not sure about products saving, but I think it could be the same.
Hope this info will be helpful.
In case I'll find the solution - I post it here.
UPDATE: I've found the solution and the reason of the problem.
It is Magento 2.1.11 bug (not present in 2.1.10) caused by the double calling of
\Cm\RedisSession\Handler::read method that initiates locking on the first call - so, the second call should wait till "break_after" config time to get needed data from Redis.
"break_after" config timings:
- For BackOffice it is: 30seconds
- For Frontend it is: 5seconds
(you can clearly see these timings in NewRelic traces)
Solution: Fix present in "2.2-develop" branch and stable version 2.2.2: https://github.com/magento/magento2/commit/aaa60b1b72bdc189b38492bd50b0ffb23101173e#diff-b4aa30666c05e391240357a7a435a7a8