The problem is that the system spans the length of the car and has three high spots: engine end, heater core, and radiator. No matter which is highest, nor where you fill, there will still be at least one relatively large air pocket. You can fill at the engine side with the radiator cap off (per the typical methods found on here) but that leaves air at the heater core; thus, the burping procedure.
My preferred solution is to install one of those inline "T" fittings from an auto parts store in the front trunk on one heater core line. This enables one to fill from the engine side, vent the air at all three high spots, and fill the whole system in one step. In addition, I don't trust the plastic caps provided with those tees (I tightened one too much and split it out), so I got a brass one from the hardware store. After I replaced the plastic cap with the brass one, I've had no issues for years with this system. But, if you need to keep it 100% stock, you need to follow some procedure to get the air out at all three high spots.
Tom
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1988 Fiero GT
Custom Corvette / MR2 electro-hydraulic power steering
17" rims covering up 11.25" rotors with Cadillac Calipers & drop spindles