You have an older stove which has 4 eyes. Replacing it with a newer cook top (only 3 eyes) would not only get rid of the oven but also a pound or two for the 4th eye.
I understand your weight concerns, I had them too. I was able to drop about 200#. I swapped the 3/4" stall matts in the bed for 2" insulation board. Works great. That was about 100#. I removed an 11" queen memory foam mattress and 4" topper and put in a 6" full memory foam. Wife says it's cozier and she has a place for shoes. Also removed the TV cabinet and roll out shelf since we have a flat screen.
I'm still about 400# over on the specs. After reading everything I could find here and verifying the info everyone submitted was accurate, I upgraded springs and tires. My axle can handle it and the brakes can stop much more.
As with you, we live in the south, the AC stays.
I don't know your vehicle specs, but if you remove too much more you might turn it into a popup.
Good luck with the weight reduction project.