Have you brought this to the attention of the mechanic who installed the engine in the first place?
There are also users on here who have in the past successfully installed versions of the 3S-GE and/or 3S-GTE in their cars,
LevinBZR, and
A-1 Superior Tech are amongst those, maybe you could seek them out and see if they can offer assistance.
Even if they can't help you troubleshoot, they MIGHT be able to point you to a decent mechanic.