does this 360 t chain look too loose?

Well you are looking at the right thing IMO: the actual degrees of movement of the crank vs cam.

Do the following if you would not mind; this is a better test than the slack test. (I am assuming that the timing cover is off so that you don't have the timing indicator by the damper to use of timing measurements.)
1) With the crank held so it is not moving, move the cam gear back and forth to the limits of the chain slack and carefully measure how far a link moves on the top of the cam. Use the center of a chain link pin as the measurement point. Measure this down to the 1/32nd of an inch if you can please. Do you have a finer scale to use? Or a dial caliper? That would be quite helpful for accuracy.
2) Then measure the diameter across the cam gear from one chain link on the right to the opposite chain link on the left.

Provide those numbers and we can calculate the number of cam degrees of movement and then then crank degrees and everyone can say if they feel that is a good or bad number.

As for the cam button, well the setup pix above sure do look right for degreeing the cam. You'll probably have to take off the cam bolt and pump eccentric and look to see if there is a small 'button' in an enlarged hole in the cam gear on the cam's dowel pin with an osset centering hole. Alternately, an offset key on the crank for the crank gear might be used; I am not sure what is most common on these engines. It would be good to check this out IMO.