Intek 25 hp 44S9

I looked engine up on the Briggs site and came up with the number in this email title. The engine is clearly marked as a 25 hp Briggs Intek;
 
 
The problem:
New purchase; first time with any riding lawnmower---a newbie.
Engine says 384 hours.  Installed new plugs and battery and cranked it over.  Every other revolution it compresses through the carburetor. Compression checks at 150 per cylinder. With plugs out, cranking engine sounds quite normal. Put in right side plug and it compresses normally on one cylinder. Put left side plug in and it compresses quite loudly out of the carburetor as above.
I think on an automotive engine I would immediately suspect a burnt exhaust valve to be the culprit.  But reading up a little it seems that these engines might have a compression release so since I don’t know and do not have the factory engine service manual, I thought I would ask for some help before I open it up. 
Checking other items, the oil is clean and has no contamination, the plugs both show normal, equal carbon burn and there are no oil leaks.
I have to admit that I have not tried to start it because of the horrendous compression coming up from the carb every other stroke.
I would truly appreciate any help.
 

Thank you so much for the focus. I will post the results once completed.

On one of the valve covers should be engraved the model-type-factory codes along with the date code, If you post those I can look up the push rod part numbers. Also look inside the springs on the head with push rod bent to see the valve guides and compare them to the other head. You probably will find they have moved out which would explain the bent push rod. Also you need to find the missing push rod as it is inside the engine and hopefully didn't do any internal damage.