Hmm...I can think of only two ways you could get a unit to spin backwards: 1) if the swirl direction (angular momentum) of the flow entering the unit was opposite from the unit's normal rotation, or 2) the reaction force on the blades was counter to the unit's normal rotation.
The tainter gates should be imparting signifcant swirl at small gate openings. I assume you have stay vanes too. They will contribute to swirl too. Had you unstacked down to the turbine level it is possible to reverse the direction of the wicket gates, very low probability. This would impart alot of swirl in the reverse direction that could eventually be overcome by the reaction force at the runner. I could see something like this happening if you had two units side-by-side but designed to run in opposite directions, you unstack one then reassemble using the adjacent unit as a reference. If this were the case you would see a significant reduction in unit efficiency and it would run very rough.
Generation of a reaction force counter to normal unit rotation would require an extreme blade angle, well beyond vertical. This is also a very low probability probably to the point of impossible but at this point you are probably considering all suggestions/ideas. I could see a scenario where the hub seals had to be replace and this required removing the blades. When the blades are reinstalled the bolt pattern is indexed one bolt hole clockwise or counter-clockwise.
I'm not questioning the capabilities of your tradesmen here, I am just brainstorming possible causes.
Regards,
Tom Moritz
Tom Moritz
Mechanical Engineer
US Bureau of Reclamation