More research based on the Toro Groundsmaster, which is running the Renault Continental engine, indicates your mower is most likely to be the Model 327. These were built between 1985 and 1989 and Toro only lists two models, being 30781 and 30787.
Model identification and serial numbers for the machine should be stamped into a plate located in front of seat on the bulkhead.
If that is the case, then this is the Toro page you will need:-
https://www.toro.com/en/parts?SearchText=Groundsmaster+327&SelectedFilterByOption=equipment

If you are lucky, you may be able to find a secondary label on the machine as indicated in this link from JacksSmallEngines in the USA: -
http://www.jackssmallengines.com/jacks-parts-lookup/toro-model-locator.aspx

If the information above is correct, your Renault engine number should be something like R08-D15-2002.

Operators manual for the Model 327 (link below) is 52 pages and has troubleshooting information that may help. Also make sure the correct oil is used in the Hydraulic system to ensure correct operation. In this link, they indicate the Hydraulic Oil used is either 10W-30 or 10W-40, not Hydraulic Fluid as you would expect, but that is for the model I selected, which you will need to verify.

https://www.toro.com/getpub/7671

I'm still unsure of the transmission manufacturer, but it may be one built in-house by Toro. If you can confirm your machine information, then it may pay to send an email to Toro about the loss of power through the transmission and see if they will reply and post back resolution to assist others.

Environmentally friendly recycling at it's best