A small, thin LCD for my device
Why too thick?

Probably because the displays that came out were that thick, became widely used, then became the defacto standard. e.g. why make another size if it can't be used for a replacement.

Alternatives?

How about this:

http://au.element14.com/midas/mccog21605b6w-bnmlwi/lcd-cog-2x16-neg-stn-w-b-l-i2c/dp/2063209

Slightly outside your range - 50mm x 20 mm x 6.3mm - though.

Nokia LCDs

My old Nokia is still going, LCD just fine, 13 years old. Of course that is just anecdotal evidence.

SMD soldering

Watch this http://www.youtube.com/watch?v=3NN7UGWYmBY