A clicking sound is usually an indication that a starter solenoid is going bad. The solenoid is a big electric switch that handles the heavy current on the starter. After hundreds and hundreds of activations, the contacts on the copper plate start getting burned and pitted which lead to sketchy contact.
A new starter shouldn't have that problem though, unless there is a separate solenoid switch between the starter and the battery. If there is a remote solenoid, I would suspect that first. If there is not, I would go back and tighten up the main ground wire and the big hot wire on the starter, as the clicking problem indicates enough voltage to activate a solenoid (the click) but not enough voltage to overcome and dirty or bad connection.
Poor ground, check all the ground straps and cables, make sure they are tight. 90% of the time with a well charged battery when you hit the starter and get a click and then nothing it is a poor ground connection.
I recently replaced a starter on my 1986 Catalina 30, w/ a universal 25, where part of the housing broke right off. Two weeks later the same thing happened to the replacement starter. Mechanics seem baffled, they mentioned it could need a shim. I'm not sure how that would work.
The first starter that cracked ws in the boat for 3 years w/ no problems. The second starter lasted two weeks, approximately 20 starts.
Looking at the broken starters, it looks like in both cases the shaft in the starter pushed right through the back.