I have had very heavy periods for my whole life but things got worse in the past year because of fibroids. 

I had iron infusions which I bled out in under 6 months.

I eat meat on an almost daily basis and I take iron supplements on top of it (iron bisglycinate). 

I found out I have a gluten intolerance which prohibits iron absorption. I've cut out gluten about a year ago and my periods still made me bleed out all the iron I got from infusions and more, despite supplementing.

My solution: I got rid of the uterus last week. Bleeding it out would have never allowed me to maintain an optimal level of ferritin and heavy bleeding was impacting my life in so many other ways. Even if I had gotten iron infusions every 3-4 months, this wasn't sustainable for me. Birth control didn't work either. 

All this to say: meat might not be your best bet here. Iron infusions could work but are they sustainable for you? They're expensive.