Hi,
I did not see you new post for some reason, when I came back to the thread last time.
I've added a sim showing the circuit I was thinking of & the diode location, in my previous post; just the lower diode in you circuit, from ground, to prevent the opamp input being pulled negative during the negative input cycle.
It can mess up the internal biassing and cause false outputs, or even damage in some types.
A schottky diode may be advisable, as that will conduct before any possible internal junction.