I don't think it would be to bad for the engine. As you said, you should consider upgrading the radiator. By what you describe it simply sounds like the water is not staying in the radiator for long enough. So if at all possible upgrade to something with a double flow, so that the water passes the fan twice, and in effect stays in the radiator longer.

VW Golf radiators work like this, but there should be others more suitable, and looking more original, that you could use.