A hydrostatic transmission consists of 3 basic parts, a variable displacement pump section, a center section, and a motor section. The center section may consist of a casting and be incorporated with the pump and motor sections, or it may consist of hoses to carry the fluid between the pump and motor sections which are at some remove from each other. The bold words are the difference between a hydrostatic drive and a hydraulic drive which has a fixed displacement pump and only moves the fluid in one direction requiring a directional control valve to change direction and the flow rate of the fluid going to the motor. A hydro offers better power and speed control. A hydraulic drive has different benefits.
You will note in the first diagram of this PDF for the Eaton 11 that the bearing on the output shaft is open faced to allow drainage into the final drive reservoir. It is not a stand alone hydro as used on GT's, but may be available in a configuration that will allow it to be used as a stand alone unit on some other piece of equipment.
On Page 3 of this PDF are diagrams of the 3 configurations of the Sundstrand Series 15 hydros. The split system, which will work for your project and which I noted other components earlier that will do the same in a closely related fashion, is represented in the top 2 diagrams. The inline version and the U version are both like the Eaton 11 in that the case drains through the bearing on the output shaft into the final drive reservoir and is not as easily accommodated for your purpose. I believe that both of these (the inline for sure) are also available in stand alone configurations, Finding one may be considerably harder than finding a flying pig.
As coldone mentioned, the inline version can be found in the MF1655/1855 GT's, as well as the JD 400 and a few other brands.The U version can be found in several JD 2XX, 3XX, and 4XX GT's, as well as several other brands. The split system is used on some golf course maintenance and other equipment ,
Coldone, you got it. As long as the motor is reversible and has complementary specs with the variable displacement pump, it will work, just not quite as well as a piston motor. A cushion valve (cross line relief valve) is recommended to dampen sudden control movement and other pressure spikes.