In 1935 Robert Marshall, Benton McKaye, H. C. Anderson, Harvey Broome, and Robert Sterling Yard got together to discuss their common vision for wilderness and the threats to wilderness as they saw it, and with that meeting founded the Wilderness Society. Could that original meeting throw some light onto "no other form of mechanical transport"? Well as it happens the minutes from that meeting still exist, and while there is no smoking gun I think those minutes do clarify some things.
First they recognized that wilderness is a spectrum and they identified five types of wilderness.
The dominant attributes of such areas are: first, that visitors to them must depend on largely on their own efforts and their own competence for survival; and second they be free from all mechanical disturbances.
For Wilderness Zones,
Such Zones not only are primarily free from man-made sights and sounds, but also permit long journeys under the impetus of one's own energies instead of those of a machine.
From these excerpts it is clear that being human powered is critical. Like I said the minutes will not clear up all ambiguity and I'm sure references to mechanized and machine will reinforce the opinions of people opposed to bikes in the backcountry
Later on they list mechanical and modern invasions they were concerned about
(c) Except as specifically provided for in this Act, and subject to existing private rights, there shall be no commercial enterprise and no permanent road within any wilderness area designated by this Act and, except as necessary to meet minimum requirements for the administration of the area for the purpose of this Act (including measures required in emergencies involving the health and safety of persons within the area), there shall be no temporary road, no use of motor vehicles, motorized equipment or motorboats, no landing of aircraft, no other form of mechanical transport, and no structure or installation within any such area
What's clearly on both lists.
What about Railroads, cog roads funiculars, cableways, etc? Do they seem match up with anything from the Wilderness Act. Motorized Equipment, maybe; but mechanized transport definitely. I'm sure some will argue that the "etc" should include bikes, but I don't believe the vast majority of people would interpret "etc" so expansively.
Is this conclusive that the founders would be railing berms if they were alive today? No, it is clear they had concerns about modern technology interfering with solitude and nature. Still, I think it is strongly supports the argument that Ted Stroll made that "other mechanical transport" means the passive transport of people and supplies and not human powered activities.
Using their guidance, what sort of recommendations would I make for mountain bikes access? Some areas, those that are the most untouched my man should continue to exclude bikes. Trails should remain primitive without improvements other than to prevent erosion or damage. Areas where bikes have a history of existing use such as the WSAs and recommended wilderness areas of Montana and recent additions to the Wilderness Preservation Systems such as the Boulder White Clouds should have managed use to maintain these areas solitude. Other areas compatible to the restricted wild areas could also have managed use.