While the cabinet may technically have a 350kW power rating, that almost certainly is not possible through the CHAdeMO connector.
350kW charging stations provide higher power through special liquid cooled CCS cables and connectors, and I believe only at higher voltage (800V or more) that only CCS currently supports. Liquid cooled cables are required to support the higher charge current (up to 500A) to support the higher charge rates.
The CHAdeMO standard, on the other hand, lags well behind the CCS standard. CHAdeMO 1.0 (which is likely what we see at most charging stations) is limited to 500V/125A, or 62.5kW (although effectively this is a 50kW charger as vehicle battery voltages in this class are 400V. There may be some CHAdeMO 1.2 stations out there, which do raise the current to 400A for cars that can draw that much current, but since there aren't any, and with even Nissan apparently abandoning CHAdeMO, I would not count on any deployments going forward.
CHAdeMO roadmap:
View attachment 631882
CHAdeMO 2.0 support would be required to get the 350kW out of the charging station, but again, this would imply an 800V+ battery, and again, with EV makers essentially abandoning CHAdeMO, my guess is that this will never see the light of day, unless it's limited to heavy duty vehicles (buses) and heavy equipment.
Additionally, even if EA "raised the limit" going through the CHAdeMO connector past 50kW, the Tesla CHAdeMO adapter itself is only spec'ed for 50kW and will therefore never request more than 50kW from the charging station.
The only real path forward here is for Tesla to release their CCS1->Tesla adapter for the North American market.