The amount of total water in your system is not as important as the amount of total gravel to the fish poundage ratio. You will want at least 5 gallons of bio-filter gravel (less for Hydroton) for every pound of fish (fully grown weight) you plan to have in your system. Hydroton displaces about 50% of your water in the grow bed, but once it is saturated it has the same density as water for weight calculations. The inch of Hydroton above the water line weighs less than water. Gravel, on the other hand, displaces more water, perhaps 2/3, and has a higher density than water; so your weight estimates are probably correct.

Make sure that your fish tank gets good light. You will need to cover your fish tank with something (preferably a net) to keep your fish from jumping out.

Go ahead and put as much water in your fish tank as you plan on having when the fish are fully grown. That way when your grow beds all fill, the water level in the fish tank won't be too low. The more water in your system the more stable it will be both thermally and biologically. With more water (and less fish density) your chemistry changes slower and gives you more time to correct it, if required.

Oversize your water pump and put control valves on your grow beds so you can individually set their fill rates. The fish solids will accumulate in the vertical water lines feeding your grow beds so you will need to purge them every few days by fully opening the valves to the grow beds beginning with the lowest bed until the water clears and then resetting it to its previous siphon cycling position. Then go to the next higher grow bed and do the same. You may find that you need to alternate this purging between grow beds as most of the solids may only be in the lower part of the vertical pipe. That way, your grow beds will each receive some fish waste solids and allow them to break down over time.

In oversizing your pump, make sure that you have enough volume to exchange the water in your fish tank twice an hour at twice the highest required head pressure (highest grow bed). Take this extra pumping power and jet-back some of the water from the pump into your fish tank for added aeration. It would be best to take the jet-back water from the highest point in your grow bed fill line. That way, you will have a greater flow up through the line filling your grow beds; and either the solids will move up into the beds, or the water flowing back down to your jet-back will have less solids in it (thereby keeping the jet cleaner), or both. The jet should be removable for easy cleaning.

Water pumps are much more effecient than are air pumps, so this is a good way to add air to your fish tank water with minimal electricity use. You will need some additional aeration in your fish tank. Also, with the added pump pressure, you will find that the grow bed control valves will not become clogged up with fish solids, as they will be pushed through the opening. Use ball valves throughout your system, as they remain where you set them. Remember, no metal in your water circulation or elsewhere in the system.

Your system looks well thought out and I believe you will be successful in getting it to work. Obviously, you will have limited vegetable grow height so you may be limited to green leafys, which is all you will want to grow until your system matures.

Oliver