EPM: Upgrade 11.2.3 -> 11.2.8 OHS greyed out and not selected

I was following Doc ID 2896100.1, as we have exactly the same issue:

Symptoms

EPM System Installer for 11.2.8 shows Oracle HTTP Server will not be updated and cannot be selected

Changes

 EPM environment had at least 2 prior updates applied pre-11.2.5 and then 11.2.8 was applied:

11.2.[0,1,2,3] -> 11.2.4 -> 11.2.8

11.2.[0,1,2] -> 11.2.3 -> 11.2.8

11.2.[0,1] -> 11.2.3 ->11.2.4 -> 11.2.8

Cause

Issue caused by missing OHS reference in .oracle.products file.

Nevertheless, provided workaround does not work, as after launching EPM System Installer version 11.2.8, "New Installation" option is greyed out.

Any suggestion how to solve this?