It is usually the valves needing adjustment, not a broken compression release. You would need to remove valve cover, and very carefully watch the valve movement as you turn the engine by hand, and watch for the slight bump on one valve. This is the only way I know to truely accurately test. I have done many valve adjustments over the years, and few camshaft replacements due to a broken compression release.
As far as removing the transaxle and cover for neutral issue. That would be a big job. You have to remember this mower is probably worth say $500 bucks working 100%.