the issue with this is beagles can dig. ALOT. so u HAVE to have some hardwire cloth or whatever under the run/ ground so they cant dig into itI am all about dogs and chickens and may come from a very similar background. Also a doc.
Consider a perimeter of hot-wire around pen if dogs not given total access to it. Properly placed can keep predators from defeating your kennel panels and corners. I also employ electrified poultry netting at times to protect free-range birds. Your dogs will still have the alarm function. I have also used baby monitors and toyed with webcams more than once to check on what is going on.