@arazmj
A quick relatively inexpensive thing to try would be to get a pair of RCA spliiters, some screw terminal RCA plugs and a carbon film resistor kit.
This will allow you to quickly and easily play with loading the primary of your S1. The goal here is to reduce the output of the S1 by about 50% (6dB ) and placing the RCA adapter into the S1 and the tonearm into one of the female sockets will allow the second socket to house The screw terminal jack with a desired load resistor. This will directly place the chosen resistor across the cartirge in parallel with the primary of the transformer.
This is where the heresy begins.... I would suggest starting with 10Ω which will set the gain of the 1:13 transformer to something more like 1:6 or 1:7 to see if this solves your overload problem. I do want to be clear that is is not transformer overload that is causing your problem but feeding too high of a signal voltage into your MM stage. The primary loading, aside from reducing gain will have minimal impact on the sonics of the transformer and the heavy load has a reasonable chance of improving tracking ability.
The resistance value can be played with and while 10Ω should net you 6dB more input overload while aggressively loading the cartridge and 27Ω will split the difference and net you around 3dB of overload headroom and load the cartridge at a small multiple of the 8Ω internal impedance.
dave