> Is it so hard to accept that "momentarily" refers to the period of time before arriving, rather than after arriving?

Yes?

I don't need to make up a different subject for the sentence when it's laid out precisely. If it were "I'll be there briefly", would you still try to contort the words into something like "The time required to get there will pass briefly"?

(Though to argue the other side, "I'll be there shortly" doesn't bother me in the least...)