I am looking for any large or medium SUV, any make, or model, 2002 or later with the following:
First choice is noninterference engine and timing chain.
Second choice is noninterference engine and timing belt.
Must have at least 2500 pounds towing capacity.
Does such a creature exist?
Yes. There are many as I am not aware of any V8 engines that are interference. So I think you would be safe to go for anything that has a v8 or larger. They also meet the timing chain requirement. Another gain with the v8 is its ability to tow at least the 2500 lbs you are concerned with. However please refer to each vehicles manufacturer recommendations on towing capacity.