Honestly, I would try again. On RAMQ website, it's clear that temporary workers are eligible. However, in another section, there is a mention of the duration of the employment.
Foreign national in Québec as a temporary worker
- the original of an employment authorization issued by the Canadian immigration authorities allowing you to work in Québec for more than 6 months. The authorization must indicate the employer's name and the place of employment.
I remember someone in Ontario got OHIP with a letter from the employer stating he intended to keep that person as his employee for more than 6 months. Maybe with a letter stating also that the employer intends to keep you for more than 6 months is what you need for RAMQ. The letter should also state that you work as full-time.
Definitely, with AIP you will become eligible, but you should be able