Wahsayah, "your" setting for ASW helicopters was the most common setting for that kind of unit until it was noted, that the "detect invisible"-flag for air units in a Civ 3 air-unit reccon function is only working if the reccon-mission exactly hits the tile with the location of the submarine.
This means, the ASW-heli with an reccon-air-mission is covering only one tile where it really can detect a submarine, while a moving sea-unit with the radar-flag and the "detect invisible"-flag covers many tiles where the unit can discover submarines. That´s why many modders set ASW-helis as sea-units. So Wahsayah, please post, if you have tested, if this setting now really covers the detection of subs in every tile of the reccon-window a reccon-air mission has.
If the detection of submarines for every tile of the reccon-window is still not working, there is another setting for ASW-helis, that could be tested:
If the "immobile-flag", characterizing normally air-units in Civ 3 is removed, the air-unit can move over the map like a sea- or land unit and with the radar-flag and the detect immobile-flag it should discover subs like a sea-unit. The backside is, that this unit can be destroyed by any unit that only has to draw on the tile with the location with the mobile air-unit. That unit could even be fitted with the "rebase"-flag and the "blitz-flag". If the movement of the mobile air-unit is set to the "All-tiles as road"-flag with a lower movement rate and the AI would use the last move of the blitz-option for rebasing that unit, this could be an interesting setting for an ASW-heli. I haven´t tested this setting, but I´m more than sceptical, that the AI would use this setting correctly.