Core/Freeze Plug blow out

I replaced a couple of leaking block plugs on my '77 360. Used the 1 5/8", Doorman 555-030. It shows the open end dia to be 1.643 with the closed end diameter, 1.63. Heigh is 0.50 This plug dropped in with not a lot left to drive it in. I tapped it in with the rim being a bit more than flush, gauging it on the others that were installed when engine was rebuilt. I bought the engine already built. Ran it up to operation temp and drove it with no problems. Stopped, let it cool down, and took it for another run. Dropped the hammer and blew the plug out.

Has anyone else run into this problem? Does the plug need to be driven deeper into the block? I see that Doorman makes a 555.068 in a 1 41/64. 1.647 on the open end and 1.635 on the closed end. It is a more shallow plug at 0.360. Ideas?