I tried this approach and the top ring of the sleeve broke off the liner and the liner started to move down. Is there any harm in pushing the assembly (sleeve and piston) down the bore if the top ring has already popped off? There is no way to push it up without damaging the rod that's still connected...
The piston/rings are obviously seized to the cylinder wall since you've broken the lip off the cylinder sleeve while trying to free the piston. Assuming that you have disconnected the connecting rod from the crankshaft, removing the piston/rings/sleeve as an assembly seems to be required, where using a little ingenuity you could fashion a special tool to drive the cylinder sleeve up and out of the block. If all else fails, you could also use a piece of hardwood shaped to match the curvature of the cylinder sleeve to drive it out with. Note that driving the piston/rings/sleeve down could cause damage to the block because there is likely a jagged edge remaining where the lip broke off the cylinder sleeve.
Alternatively, you could simply leave the piston/rings/sleeve assembly in place and let the machine shop handle it using a shop press.