There is nothing wrong in principle with the configuration you are using, that's how bidirectional thyristor drives work.
The likely causes of problems I can think of are either not leaving enough time for thyristors in one bridge to turn off, or the lack of "snubber" components to limit the rate-of-change across other thyristors when some switch on.
Are you using the AC zero crossing to synchronise the thyristor firing control with the AC cycle?
You need to either do that and wait until after a zero before triggering different thyristors, or leave more than 10mS so any previously triggered have switched off at a zero crossing.
For snubbers, add four R-C networks, eg. 0.1uF and 100 ohms in series, connected from each AC in to each DC out point.
Thyristors can trigger spontaneously if the voltage across them changes too fast, due to internal capacitance from anode to gate etc., the Dv/Dt parameter in the data - as low as 50V per microsecond for the ones you are using, without a gate-cathode resistor. Snubbers slow the rate of voltage change, as well as reducing interference and improving switching in the case of an inductive load.
Adding eg. a 150 Ohm resistor between gate and cathode on each thyristor may be a good idea, it is recommended in a lot of applications.