If it only says you can ride at short distances I would say no running. I noticed in your other post that you are losing weight, but until you have reached a size that is a little easier to carry I would stay away from running.
*sorry if I sound mean. I definitely do not mean it to be that way at all.
I am 6'8" and pretty close to 300 myself and I find that if I condition my horses and I don't try to ride one hard day after day my size has little effect on them. It also has alot to do with how well you ride. If you flop around like a bag of potatoes you will wear out and sore your horse faster. If you ride a quality saddle with quality pads and you ride well then you should be fine. Pay attention to your horse and let the horse tell you when it is struggleing.