Thank you for your information. Now, I understand what the issue is.
The commercial flow is as follows:
Toyota USA -> (commercial shipment) -> TMC -> (non-commercial shipment) -> TMAP
In order to simplify operations, the basic concept for H-order is to use only 1 invoice (i.e. shipper: Toyota USA on behalf of TMC, consignee: TMAP) for both export customs in the US and import customs in Thailand. If absolutely necessary, we may have to make exceptions and somehow arrange the 2nd invoice, but it complicates this global process significantly.
Tomorrow, I will discuss with TMC regarding the new option you mentioned because, in the end, TMC is the final payer for import duty & tax in Thailand. I will keep you updated.