Welcome to the club bro.
More experienced Paleo Members could tell you better about your Stomach feeling, but I could only say about myself that digesting raw grass fed beef is the easiest thing on stomach (sometimes in the beginning, there may be some diarrhoea, but it is good while it is only the detoxification of stomach).
I cannot tolerate free range eggs (but there are many who could do it). For me, the eggs should be pastured ones.
After eating first time the raw meat, the next steps which helped me:
(1) Fats: The amount of fats in your trimming is not enough. You need much more fats on this diet. Grass fed Fats bring wonders. Back fat, suet, bone marrow, brain. Fats are absolutely necessary.
(2) Organ Meat: Also absolutely necessary are organ meats. Not so much, but still perhaps 25 gm per meal. Heart, liver, tongue, kidney (and later sweetbreads too)
(3) Dairy is not optimal. If any, then raw milk kefir (good for the beginners), raw milk butter (good), raw milk cheese.
For some people it didn't help, but for me (and many others) immense help came from the "activated Charcoal" in the beginning. Both inner and outer use. Activated Charcoal proved for me much much better than the healing clays.