As you mentioned, I found it worked easiest to put the center portion in first. Use a water-soluble lube (such as KY) because the flats of the inner portion of the bushing need to line up with the flat of the control arm.
I then used all-thread, nuts and washers, and appropriate 3/4" drive sockets in order to press the caps onto the center portion of the bushing, one at a time. This is the same method shown in the FSM and using the factory tool.
http://www.startekinfo.com/StarTek/outside/12253/program/Chassis/33-520.pdf
From your description, it sounds like one of the caps became deformed. This is usually due to pressing on the end of the cap, rather than the outer lip as shown by the red ring in post#10 of your installation reference link. (This is where the 3/4" sockets come into play.)