I can tell you my experience with valve train problems on the M880 that I have since fixed.
First, the engine used to blow blue smoke out the tail pipe almost every time I started the engine, but not so much after it ran a while. Secondly, the lifters were quite noisey at start up sometimes, more depending on how long it sat between starts. Both these problems probably stemmed from the fact that even though these trucks had low miles on them, they sat unused for long periods of time. This likely caused the valve oil seals to harden and crack and the lifters to build up a film and stick.
The solution was pretty simple: I went in and replaced all of the valve stem seals, (this worked like a charm for curing the blue smoke at start up), and secondly, right before an oil change, I poured a quart of engine de-sludge-ifier into the oil and let it run at idle for about five minutes.
*It is very important that you don't rev the engine or put it under load while this stuff is in there since it acts to thin the oil and you could damage the engine*
This worked like a charm to quiet down the noisey sticky lifters, and I've never had the loud clacking at start up since.
Now I'm not so sure about your broken push rod. I'd want to know what caused it to break in the first place. They don't snap without a reason. Was the engine over revved? Was there a foreign object stuck in the cylinder?
