DAS .. point 1 .. the trips on UA I have made to Buenos Aires have always 'common rated' Montevideo on price, as the UA plane continues on to there! It is actually the shortest It'l flight UA makes, and takes about 20 minutes or something! So, unless you are dead keen on doing it by ferry, at your cost, I suspect your ticket will allow that destination free, and you'll get extra miles, and the stopover in EZE will be your legal stopover.
Hotels are tough there as they have a strong currency, pegged to the $US. I ended up needing to do as you mention, use those 50% off UA coupons, and stayed at both Sheratons alternately and winced about the price. Best I could find.
Remember the Manuel Tienda Leon airport bus is basically a free city tour from EZE in a modern big AC bus. EZE is in the countryside basically! They take credit cards for it, at their airport desk. It does via the downtown Dumos Dumont (sp?) domestic airport, and stops (and leaves from) nearly right at the door of larger Sheraton. Price very cheap .. about $8 as I recall. Which in BUE is a BARGAIN! Some trip notes here:
www.GlenStephens.com/penguin.html