1991 Acura Legend Overheating

I have a 1991 Acura Legend Coupe LS that had a small radiator crack-leak for about a year which I repaired with epoxy. Eventually the engine temp gauge started showing overheating levels and the radiator crack was now "cracks" (always on the top of the radiator body). I attempted to epoxy the new as well as old crack but the engine kept overheating and I was constantly refilling the water deficit in the radiator. Subsequently I bought a Bars Stop Leak product that had chunks of particulate in the bottle which I put in the radiator as per the labeled instructions. This didn't solve the problem and the engine would overheat some and the radiator would lose fluid content. I was constantly topping off the radiator water level to keep the car going. Ultimately I bought a new radiator and installed it. I flushed the engine cooling ports with a garden hose once the old radiator was off and the old thermostat was removed. The initial flush liquid was cloudy but then came out clear watery in appearance but I continued the water hose flush for about 5 minutes. I installed the new radiator and refilled it with new 50:50 green antifreeze which "cooked off" or was lost via an overflow or drain hose back ~12"-15" from the radiator at the bottom side of the engine compartment (I'm not sure what caused the fluid radiator fluid loss). So I refilled the radiator with hose water only. I then had to add some water after every short distance drive to maintain the radiator fluid level. But about 2 wks. Post radiator replacement the radiator fluid level stayed full and the engine temp gauge registerd at a mid-gauge reading so I thought the problem had finally reached a homestatic equilibrium--challenge solved. Unfortunately the engine has been overheating again but without loss of radiator water volume. It only takes about 2-3 minutes from starting the cold engine until it begins to climb above the middle temp reading on the gauge then it will reach near the high end of the temp gauge in another 3-4 minutes so I have to pull over and let the radiator fans cool the temp some. I'm wondering if the water pump and/or the head gasket(s) are bad. There is no water or foam in the oil on the dipstick.
Thank you for your due diligence,
Richard