The OSHA standard requires ("shall") operator training and further requires that the training includes the "Operating Instructions" (i.e. the Operator Manual that comes with the truck). I would look there first for instructions on how high to carry a load while traveling:

OSHA 1910.178(l)(3)
Training program content. Powered industrial truck operators shall receive initial training in the following topics, except in topics which the employer can demonstrate are not applicable to safe operation of the truck in the employer's workplace.
Truck-related topics:
1910.178(l)(3)(i)(A)
Operating instructions, warnings, and precautions for the types of truck the operator will be authorized to operate;

ANSI/ITSDF B56.1 (which OSHA requires conformance to) further states:

5.3.10 Travel with load-engaging means or load low and, where possible, tilted back. Do not elevate the load except during stacking.

and

5.3.18.(c)/5.3.22(c) - Tipping forward can occur and its likelihood is increased under the following conditions, or combination of them:
(2) traveling with the load tilted forward and/or elevated

and

5.3.22.(b) - The likelihood of lateral tipover is increased under any of the following conditions, or combinations of them
(2) traveling with the load or load handling mechanism elevated