Don't worry. I'm on the same visa. Same situation. Do your 90 days (visit immigration about 1 month after you arrive they should guide you through the process) then covid extension then family visit visa. Gives you well over 6 months stay.
I had this problem before. I'm afraid it is very difficult to get covid insurance for a specific number of days. They seem to sell in groups like 1 month 6 months 1 years.