I was in the same situation years ago with my 617.912 car. It turns out not many people know much about the injection timer, because there is not much to it. 2 springs, 2 weights that advance pump timing as RPMs increase. Inside the springs there are 2 stops that serve to effectively limit the degree of advance to a fixed amount. When paying close attention, rotating the engine by hand, it is just possible to hear them slide up and down.
Do not worry about axial play in the timing device, the injection pump and timing chain tension keep it in its place while the engine runs.
The clip on the timing chain tightener is supposed to be sort of loose. The running engine oil pressure should keep the chain very tight while the engine is running. The play felt in the pin without oil pressure is negligible. Oil pressure keeps the chain very tight and automatically compensates for wear. If the chain was in fact rattling loose, there would likely be significant collateral engine damage. Check to see if it the chain is excessively stretched or the tension is losing pressure. Remove the valve cover shortly after the engine is run. The chain should appear to be very tight on both sides. Any slack should receive prompt attention.