A couple of updates:
I heard back from Lion Battery. The official dimensions of the Mugen 4500 mAh battery are 2.60" x 4.65" x 0.24" (protruding from the back of the PDA).
However, the Otterbox distributor informed me that my planned configuration
WOULD NOT fit into the Armor 1900 case. Maximum possible dimensions are apparently 147 x 77 x 20 mm. (not 23.5 mm). This contradicts the information stated in the 1900 compatibility list, available as PDF document from otterbox.com (141 x 87 x 23.5 mm). Yet another version is given on the Armor 1900 web page at otterbox.com (141 x 89 x 19 mm) ...

I will email Otterbox about this and let you know if I learn something.
Possum: dimensions of the HP 3600 mAh battery... that's another well-kept secret. Well, here they are: 2.9 x 2.1 x 0.46 in (66 x 60 x 11.65 mm). The ordinary 1800 mAh battery is 0.23" (5.85 mm) thick, which might be helpful in estimating how much does the 3600 mAh version add to the thickness of the setup.