I assume you went to the service centre and they advised that they don't offer the service of downgrading firmware?
Anyways, manual flashing is actually very simple. You need to find the 4.3 firmware FTF file and then use Flashtool to flash. Ensure that you untick the "Wipe data" option during the flashing process.
I searched the XDA threads for local 4.3 firmwares, and can only locate a 4.3 firmware for Singtel here (which would come with all those Singtel pre-installed apps):
[STOCK ROM][FTF] Xperia Z (C6603) 10.4.1.B.0.101 Singtel (1270-0743) - xda-developers
If you prefer a more generic firmware without all the pre-installed apps, you can try the
10.4.1.B.0.101 Generic Ukraine firmware. Besides the default language setting at 1st startup, there isn't any difference between this firmware and a generic SG one.
Use
here for how to use Flashtool to flash firmware (includes video guide).