Pretty sure you just disconnect the hose and pour in fluid till it won't take any more. But it does sound messy. But hey, you're Gen 1 and I've only done the Gen 2. Probably 10 times dammit.
So it probably really doesn't matter which hose on the heater core I'm guessing. Also, someone mentioned fill with the upper radiator hose off until fluid runs out, then connect and fill until it won't take anymore. I'm guessing this is done with the car turned off?
I went aftermarket aluminum a few years back, and in a year I had a leak. It cost $100 to have it repaired and it never cooled the same as before. Now its starting to leak again.
Next time I'm going Mopar.