I would rather not carry at all than carry a pistol that weighed more than a few ounces. I tried running with my keltec 9mm and it's too uncomfortable. On top of that, I don't see how you can conceal a pistol much bigger than a subcompact in comfortable running clothes when it's in the 90's.
It's not a matter of gut vs gun or not being able to handle the extra load. I ruck with a 60 pound pack about once a week. Running is different though. I have to take a PT test twice a year that counts towards promotion points and plays significantly in the selection for which soldiers get selected for schools. I want to be light and unencombered, and I would love to see how you do that with a .45, spare mag, back up pistol, cell phone, and collapsable baton. Lets be realistic, I've run thousands of miles over the years and the incident I related is the only time I was actually concerned I'd get bitten. A little .22 is plenty for a low scale threat like an over protective and excited dog and many would say even that is overkill.
I'm not saying that I doubt any of the members here that claim to work out while carrying large pistols, I just have never met anyone else in real life during my years as a soldier, collector, or cop that did.
I really think that a blank firing gun would scare off most dogs that are just satisfying their chase instinct and at worst would take a nip at your ankle. I choose not to get nipped and a little .22 served my purpose just fine.