I know nothing about off-road use and which are the best tires. But low tread means less grip on the road, especially when it gets low as I have indicated. I hear what you are saying that your jeep is your rain vehicle, but just think about being 100 miles from home and it rains. Also,even though rain (and snow-but not in Texas) may increase the gripping, same is true to a somewhat lesser degree on dry surface. Hydroplaning is partially identified with low treads.
Two tires that are not identical on the same axle is dangerous--and very dangerous for you to put different size tires on the same axle. In some States that is against the law. You are indicating that you " bought it like that" as if that makes it safe and nullifies the safety concerns. I am not sure what kind of tires you have in terms of lifetime wear, but 5000 miles does not sound like much rubber. Over 5/32 would be the test measurement.
PS--as long as you are going to look at the tires, one other thing that many people ignore is the DATE of manufacture on the tire. Look at that. I would suggest that if you have a tire on your car with a manufacture date of over 4 years old, consider replacing. If it is over 6 years--I would consider it not safe (although some people would disagree on age). What happens is the rubber (sidewalls) deteriorate, sometime spotted in fine cracks, which means the tire is subject to major failure such as blow outs. At 60mph (or 80 mph) I do not want to have that tire on my car--I value my self and the car more than allowing those to be my wheels.