The Greenfield mowers are locally designed and made. I don't think there are many standard parts in them aside from engine, belts, tyres etc. However the tie rod ends may be standard. (Most ride-on mowers sold here under local brand names are actually standard American mowers rebranded, but Greenfield doesn't do it that way.)
There are four requirements for an adequate steering system for a ride-on mower:
1. No slack.
2. Correct geometry.
3. Reliability.
4. Satisfactory feel.
Any way of getting those four things, can be considered a valid solution. On your semi-homemade system there may be enough adjustment at the various tie rod ends to achieve the correct geometry. Whether there is slack, though, is another question. Many ride-ons don't seem to be lubricated regularly, and get seriously loose over a period of years.
