Is there a mathematical formula that determines lifting ability for a precise Strength rating (e.g., Rm 29)? If not, is there a mathematical relationship between the gross column shifts (e.g., an exponential progression that gets rounded to the easily-remembered numbers)?

Not really, there isn't.

The difference between RM 29 and RM 30 is that RM 30 can do 1 point more Health damage with a punch than RM 29. Both have an equal chance of automatically lifting up to 400 pounds (Good), rolling a Green FEAT to lift between 401 to 800 pounds (Excellent) rolling a Yellow FEAT to lift 801 pounds to 1 ton (Remarkable), or rolling a Red FEAT to lift 1 ton and a pound to 10 tons (Incredible). Remarkable strength is not going to lift 10 tons and a pound to 50 tons (Amazing) ever.

There's also a difference between lifting and carrying and throwing. It's probably out of the question to carry around weights that would require a Yellow FEAT to lift every round, and heaving weight to toss that would require a Red FEAT to even lift is probably just not doable if you want to keep the FEAT intensity scaling intact.

Are there any articles or interviews by the game's creators that explain why they chose the CS numbers? I tend to assume there was a logic to it, if for no other reason than the RPG industry was built by math-loving gearheads back in the day, and the underlying mechanisms they designed often involved math concepts with a thematic facade applied.

Thus far, I've been unable to deduce a consistent progression, and it seems like every time I hit on an idea, it gets disproven half-way through the chart. Even more strange is the lifting progression -- x2, x2, x2, x2, x2.5, x10!!!, x5, x1.6, x1.25 -- which makes no sense, unless Marvel has some in-universe explanation for there being a void between characters who can lift a ton and those who can lift ten.

All of the weightlifting numbers come from the old Marvel handbook numbers. They divided people into classes. Or at least that is my theory. Those numbers have been since a long time ago relative to each other and not an absolute terms. So, I'm not even sure in the 80s class 100 people like Thor would have really been considered only able to lift 100 tons.

Also consider the very limited number of real world objects that weigh 100+ tons that aren't a collection of parts that total 100+ tons rather than one big chunk of something that weighs 100+ tons. Sure, a jumbo jet might weigh 100+ tons, but if something strong enough to lift it picked it up by the nose or a wing or the landing gear, shifting away from its center of gravity is going to snap that nose / wing / landing gear off as the structural integrity fails at the lifting point. Too much realism in the game logically has to consider this. Sure Thor can lift a jumbo jet over his head, but he probably ought to roll it into a ball and crush all the people inside of it to death to keep all that weight compressed into a manageable center of gravity