Try adding an aquarium air stone to your res as it is right now then, if you think you want to keep using it, and try to figure out how to drain it better.
Oaky. Let's think what your other options for salvaging your system are.
A simple pump, sitting in a 5 gallon pail below your pot, and plugged into a timer to run every ~4 hours or so, pumping to drip emitter stakes or even just tubing secured so it drips at the base of the plant, is a simple and cheap automatic drip system. You can do drip-to-waste or recirc. drip on that system.
For a simple to build and maintain hydro, that is not ebb n flow, go into the grow log section and look for 'stinky kinda likes the darkside'. That style doesn't require an air pump because the water is constantly moving around and mixing in atmospheric gases. Transplanting- because of your drainage problems, you might be best off transplanting. You will have to be careful not to damage the roots. Perlite falls away easily, so be careful. Another pair of hands to support the root ball as you do a pot swap would be helpful. You can transplant into promix or coco without washing the roots, and that is what I would do if those were my plants. Both are soilless mixes and pretty compatible with perlite. If you choose coco, keep using calmag on it! But anyway, the roots will quickly grow into the surrounding medium and your watering woes will diminish.
Yikes. You have quite a tough situation to fix there. Sorry it's turning into such a clusterfuck.