Try chewing meat thoroughly to the extent where it is liquified and perhaps this is impossible with red meat unsure. And eat little bits at a time. Chew very small bits into a liquid and do this over the course of an hour to eat a portion of meat that is small to medium in its portion. Perhaps have some fruit to eat with the meat.
I am not sure to what extent your problem with digesting meat is so try this at your own risk and start off very small to see how you react and if you increase portion size do so gradually and by portion size I am talking about the overall size of the portion. I am not suggesting you increase from eating small bits at a time.