Spongy pedal after big bolt pattern conversion

You are right the only way to bleed this type of caliper is with a Phoenix injection system. Thats all we use in our shop.It forces the air up the line and out the master cylinder.
You still have air in the system. The lower bleeder on the caliper is tough to get the air out. There is a brake bleeder that pushes the fluid up to the master that should fix this problem. Be sure the rear brakes are adjusted properly with a slight drag.