here's a good watch. 45mm case, thicker than your Hamilton (it sits high off the wrist due to a rounded caseback).
http://www.jomashop.com/breitling-mens-watch-a1338012-f5-132a.html
here's another, don't be shy because its 46mm, it wears smaller.
http://www.jomashop.com/breitling-naviti-a2432212-b7-443a.html
I tried one of these on once, it was nice, also thick.
http://www.jomashop.com/bvlgari-bvlgari-mens-watch-bb42wsldch.html
Also, I am partial to these, they are 46mm but do not wear like they are. you can try mine on if you'd like to see if the size is right. Then again, you may not like the trigger.
http://www.ebay.com/itm/Graham-Chronofighter-OverSize-Overlord-Ref-2OVAS-B03A-K10B-/281169950774?pt=Wristwatches&hash=item417708f836
Here is another watch I live. Really tall, and only 44mm
http://www.ebay.com/itm/NEW-Ennebi-Fondale-Ref-9682-Titanium-44mm-automatic-13J049-W-/181275830525?pt=Wristwatches&hash=item2a34e1a8fd
BTW, What Hamilton did you buy that is 16mm tall?