Decreasing the resistance between G and T1 increases the triac limit of dv/dt though it increases the driving current which in turn increases the phase at which the triac is on (after zero crossing).
On your schematic, I read 620. If it means 620R (620 Ohm), it is relatively high (it has no significant effect).
The internal G-T1 is somehow like two reversed diodes connected in parallel (this can be checked using a multimeter).
So, the excess driving current for the 620R is 1/0.620 (assuming Vd=1) ~=1.6 mA only
A value of 33R (instead of 620R) may be needed here. The excess driving current for the 33R is 1/0.033 ~= 30mA. If the delayed phase is acceptable in your application, MOC can deliver this added triggering current.
For instance, the resistance, 620R, between a phase and MOC could also be reduced a bit if necessary (lower limit if 240Vrms is 450R with a margin around 25%).
One more point, here R8 is connected to U4 and U5. I personally prefer driving a MOC couple, as U4 & U5 for example on your schematic, by two separate resistors instead of one.
Hope this helps.
Kerim