Lionel Hiawatha vs the CW-80 transformer

A few months ago I purchased a reconditioned pre-war Lionel Hiawatha Milwaukee Road set (250-E locomotive, whistle tender, three coaches and two attaching vestibule (?) pieces).  I cleaned the motors on the locomotive and whistle tender, and lubricated the loco's gears and wheels before putting the loco and tender on the test track.  The engine ran reasonably well, but I noticed that occasionally the green light on the CW-80 transformer I was using started to flash.  In the past I had only seen that happen when a car derailed and there was a dead short across the track, but a quick google search revealed that the light could also flash if too much power was being drawn.  I wasn't trying to sound the whistle at the time, so the whistle motor wasn't drawing power.  The test was done on level, cleaned track, with none of the coaches attached.

Does anyone know if the pre-war Hiawatha sets required a more powerful transformer, or should 80 watts be sufficient to run it?  On a related note, I have been looking at Lionel ZW transformers online.  I've seen some refurbished models on the tinman3rail website that cost more than the "as-is" or "works" models I've seen on ebay, but appear to be ready-to-go when they arrive.  Does anyone have any experience with the refurbished ZW's from tinman3rail?  I've only purchased track from them before, but haven't had any issues with them.  Thanks.