...Have they tried it with a weightless balloon?  Have they measured how far up relative to the suns they are?  It's triangles, for goodness' sake!  Trigonometry isn't that overwhelmingly difficult!

Sure, they know how far up the suns are. Here's a chart on the heights of various suns observed over a certain period; they're normally distributed about ten miles up. They've invented triangles. They just haven't gotten a hot air balloon up that high. Not with a person in it, and they have no other way to take observations.

...she is now contemplating metal-framed vacuum-filled zeppelins with density-troportation 'ballast'.

They don't appear to have the concept of vacuum.

...Surely, surely they have density, though?

That they do.

Can they make something have a density of 0 g/cm^3 with troportation?

Nope. You can only troport solid objects and you can only swap, not transfer, density.

...Can you transfer mass, though?

No.

...but you can swap it?

Yes.

Well, if you keep swapping masses and densities around, you can get an arbitrarily light object.

...Now she wants a balloon based on that principle, because she can.

Maybe she'll get some rocks and some string and start Making That Happen for the local kids.  It'll be a fun activity and train their troportation discriminance.

...Are there proper schools for children, yet?  And then she should probably check her mail.

Kids are taught to read and figure in the dreamward and may or may not pursue any further education once they're out.

She does not have any messages waiting at her storage unit.

Then her next stop, after making a metronome and 'balloon' to go with her clock demo model, is the bank, to see if they do business loans.

The soundtrack to her brain appears to have settled on Let's Go Fly A Kite for the walk; she certainly has the spring in her step for it.

There is a line at the bank and only one teller on duty.

She's not busy.  Or, well, she is, but not on this particular timescale.  She'll just wait patiently, possibly sketch some things, and see if there's any gossip happening (and eavesdrop), because why is there a line at the bank, anyway?  Is it payday or something?

Nobody has chosen to explain it out loud right this minute.

Eventually she gets to the head of the line.

"Account number?" says the teller.

"I'd like to open one, if you please; I would also like to speak with anyone that might be responsible for disbursing business loans."

The teller gets her a form to fill out for creating an account. "My colleague is having a baby and will be back in a few cycles."

"My congratulations to them."  Interesting.  It's surprisingly apt timing for her pitch of troportation ECE.

"Next!"

There are little tables and chairs for form-fillers such as herself.

And the form shall be filled!  What does it ask for, anyway?