You need to get a better strain of mouse then. The mice I used to breed were 25 grams at 4 weeks old. If they are ovulating and breeding, they are ready. I bred mice for 15 years and have friends that have been for 25+ years. Our females were always introduced at 28 days. You will see litters in 21-25 days. Mice and humans are apples and oranges. Keep waiting and limit your production.
If you know EXACTLY what age to breed them, why even ask people their opinion? I know it worked for me for many years, but you absolutely refuse to take my advice. It's not waaaay too early if it's been proven successful for many many years. You say the ABSOLUTE minimun is 6 weeks, I say it's 28 days.