Reverse flow undergravel filters are old school now and there are kits to convert regular UGF's to reverse flow. Oxygen in the water is the result of moving surface water or when bubbles break the surface and a CO2/O2 gas exchange occurs....so adding an inline air line in the flow tubes is really counter productive.
Taz is correct in that beneficial bacteria are somewhat opportunistic feeders and slower moving water is processed much more productively. Airflow in the standard UGF moves water slowly through the gravel bed.
Although I've used them in the past, I'm not a fan of UGF regardless of flow direction (although reverse flow is probably less problematic than regular UGF).
The trouble is with the gravel as even with reverse flow, too much waste and uneaten food sifts down into the gravel where it decays and produces copious amounts of ammonia...nitrites...nitrates. This requires routine gravel siphoning.
I converted to [deep] sand some time ago. Mulm collects on the surface and slowly decays or can be easily removed and the sand is an excellent bio-filter.
Just my $.02. If you move forward, hope it works for you.