The R-2180 is really two different engines.
R-2180A
The first was the R-2180A and design was started in 1935. P&W had too much on their plate so after a run of 30 engines from 1937-1939, the R-2180A was dropped.
Horsepower: 1200-1500
RPM: 2500-2600
Cylinders: 14
Weight: 1665-1647 lbs
Bore: 5.75in
Stroke: 6.0in
First Run: 1936
Number built: 30
R-2180E
In 1944 P&W had the idea to produce a commercial engine incorporating all they have learned over its 20 years of experience. This engine became the R-2180E. This particular engine permitted the use of reversible-pitch, full feathering hydromatic propellers. It also had some valve timing trickery to increase power. This was the last piston engine produced by P&W.
Horsepower: 1650
RPM: 2800
Cylinders: 14
Weight: 1830-1870 lbs
Bore: 5.75in
Stroke: 6.0in
Number built: 75
Diameter: 54.00in
Length: 76.00-76.20in
R-2000
The R-2000 was a further development of the R-1830 built in 1939.
Horsepower: 1300-1450
RPM: 2700
Cylinders: 14
Weight: 1570 lbs
Bore: 5.75in
Stroke: 5.5in
First run: 1939
Number built: 12,966
Diameter: 49.50in
Length: 60.70in
For books on P&W history I would recommend:
The Engines of Pratt Whitney: A Technical History by Jack Connors, 2010. Mr. Connors worked for P&W mainly in the jet age but gives a very good account of the piston engine days as well. The first 160 pages cover piston engines. Most of the info above comes from this book. You will also find a few engines that are more obscure than the ones you have listed.
The Pratt Whitney Aircraft Story, by Pratt Whitney Aircraft, 1950. This is a company published history and a great read.
I do not know of any sources that deal in detail with the R-2000 or the R-2180.
WJP