When I restored my '37 with a 216 I had to replace the head because it was cracked across an exhaust valve causing lack of compression in one cylinder. I then went about cleaning out the water jacket with the block on an engine stand. I flushed with water, blew it out with compressed air, fashioned a vacuum attachment with heater hose to stick into freeze plug and water pump holes, dug around using the smaller holes with a long screw driver, ect. There was 3-4 inches of compacted dirt/rust front to back. Finally, I started to feel I had it cleaned pretty good. Today, it does not overheat at all. I looked to see if you were in CA (and you are) because in warm climates they didn't need antifreeze and just ran water for coolant, leading to rust and particulate buildup over the years in the water jacket.
If you are persistent, with the head off, I believe you can clean it adequately without removing the block but it will be awkward to say the least. Follow the great advice to service the head now. You will get this.
Kent