You make an interesting and important observation, Bret. A closer look at the photos does indeed make it appear that what you suggest is true--that the Rushton stacks were bolted on over the straight stacks. There is clearly a space of a few inches between the base of the Rushton stack and the top of the smokebox, and the connection between the smokebox and the Rushton stack looks very much like the base of the straight stack: same flare, same diameter, same bolting pattern, etc.
I have a reprint of an 1892 book titled "Modern Locomotive Construction." The few pages on stacks don't show a cross-section of a Rushton stack, but there is one of a Radley & Hunter stack. The R&H stack comes very close to being functionally the same as the Rushton stacks, and it's reasonable to assume that the Rushton stacks were developed after 1892. The R&H stack has an inner barrel which has a comparable length and diameter as a straight stack.
So I agree that what you suggest is true: the Rushton stacks were bolted on over the original straight stacks. Even the low-profile diamond stack shown in the builder's photo appears, upon closer inspection, to be attached over the straight stack, and presumably was removable. Your further suggestion that the Rushton stacks were removed during winter seems entirely reasonable as well. Unfortunately, as you know, not many of the locomotive photos we have are reliably dated, so we can't be sure of when they were taken. A straight stack photo of No. 19 or No. 20, reliably dated and taken after the Rushton stacks were first installed, would clinch the matter.
Regarding locos 16, 18, and 50, I'm sorry to report that I don't find anything in my files that would shed any light on how they were used between 1941 and 1944, when they were sent to Peru.