Bosch2460-- You want a Maytag Tall-Tub model. I have the TOL (stainless interior) model 8951 and it cleans pots/pan/baking sheets perfectly. The capacity is amazing and it's extremely flexible for loading.
Maytag's line is a little odd---there are three top models; each is available with either a stainless steel or plastic interior. The two top models are the 8951 (stainless) and the 7601 (plastic). I highly suggest either of those.
I bake a lot as well and use the same rimmed baking sheets you're referencing. They fit with no problem. I have 13" dinner plates that fit with no problem, so I'm sure it will take your 14" plates, although you might have to raise the top rack to the upper position.
My favorite feature---one I initially thought I'd hate, and which almost caused me to look elsewhere---is the tiered upper rack. It allows you to put tall items either in the left half of the lower rack or the right side of the upper rack.
I had a TOL Frigidaire last year, and although it was a good machine, it can't clean bakeware/pots/pans like the Maytag. The Frigidaire's tub is a little shorter than the Maytag's, so it doesn't take really tall pots, etc.
I have a load in the machine right now, but later, I'll put some big bakeware pieces in it and post photos here so you can see what it will take.
Here's some info on the two Maytag's I recommend. First, the 8951:
