In my observation ABAC HR is well known among Bangkok immigration officials and she handles the visa of students and faculty. She could answer you and I hope it could be done
After you renew your passport, you can update the passport number when you apply for evaccine passport which you can apply for free until the end of this month in Mor Prom app. I got the same vaccine under social security. Same certificate which you display doesn't list my passport number but I got it listed in evaccine passport. You can get it done in three working days. Sometimes two as well if you apply around quarter to midnight.
Which part of India are you staying? Thai Embassy is in New Delhi but you got consulates in Chennai, Mumbai and kolkata. Approach them in person. They may help you since you are responsible for a minor Thai citizen.