In the 156/S-wing (at least in my experiences) problem, the symptom was a "delay". The best way I can describe it would be a "click, slight pause, then the air would flow" with an inhale. Assuming you have it assembled correctly, I'm betting that the thickness of the Trident seat is a contributor. Yes, the orifice would then need to be further out to be in position. However, it is possible that the lever is included is the issue. Finding a G250v lever might be worth the search. Again, that eBxx guy in Japan has been listing them, though it seems it is a problem for you due to your location. Not sure where else to recommend as it's different for me here in the USA.
There are some threads in the DIY discussing the lever..... There is also a tool made by Herman that is used for bending the lever, though I am hesitant to even recommend this approach, unless the only other option is to completely abandon your project...
As to the availability of the "old" poppet, they are no longer made. Anything you find is likely very old stock, and the seat may have aged to a point it is no longer functional.
Fun, isn't it?