During your necropsy you could also look for a yellowish liver for toxicity, stomach/intestinal bloat, and you could look for spotty or bloody lungs for respiratory illness. Kidneys should also be checked like liver for paleness and spottiness.
You are not stuck with hay or pellets, but you cannot feed people food only. I would suggest you look for neighbors with gardens and yards and take their weeds, fruit tree prunings, grass etc., and also look at parks and less traveled road side or hedgerow areas. Bramble vines (blackberry, raspberry, rose) are especially well loved, even though they are thorny. So are many types of tree bark, though it may not be as nutritious it will provide fiber.
Unfortunately you will have to learn what is poisonous to rabbits. As a general rule if an ornamental is considered resistant to deer it is not going to be good for rabbits either. Another tip is to learn the latin names of the plants in your area and plug them into a search engine with the word "fodder" or the word "toxicity". There have been many animal studies for alternative fodder sources, which can be old but still useful. Like me!
There are MANY MANY natural feeding threads here on rabbit talk also.