The middle terminal is hot on my 180w brick, I presume the 135 should be the same. Lionel sells a cable set 6-14194 so you don't have to cut the plug off. It includes a plug with spade connectors on the opposite end.
The terminal strip is fine, my brick is connected to a TPC unit, the TPC unit is connected to an MTH terminal strip and buss and feeders go out from there.
I recommend using at least 16 or 14 ga wire. I ran 14 ga buss and feeders and only have 4 pairs of feeders on each of my 10'x16' loops. Power delivery is consistent throughout, same at the track as it is at the terminal strip.