The line coming from the head is the direction of flow. By design, the block will mostly drain. If you put the rear tires on blocks, it will help level the block. If you have compressed air, you can blow most of the coolant out by using the fitting at the head for the heater core. I would also blow air in the top of the radiator at the inlet. With crossflow radiators, coolant will "pool" in the cores. I also recommend you syphon the coolant out the top, at the radiator cap, no mess. I use about 6-7 feet of 3/8's fuel line, the longer the better, less chance of getting a mouth full
If there is any doubt about how clean the heater core is, you might use some Toilet bowl cleaner, (the works) With a small funnel, fill it up and let it set for about 30 minutes. Both heater hoses will need to be above the level of the core. Be careful here, the cleaner is toxic/acidic.
#ad