Regarding the Saratoga, given the models available at the time, the producers did seem to make a conscious decision to give Sisko one of the oldest and smallest ships. The Constellation wasn't used at all, perhaps because it had previously been depicted as obsolete and retired in TNG, although PIC retconned that. The Oberth was just *too* weak. So the Reliant model was the only choice.
The Stargazer model had been relabeled "Valkyrie" and was going to be used for either the Wolf 359 battle that we saw on screen, or was actually used in the unused footage Rob Legato shot that was discarded for the footage we saw. Closeup, the model had originally been built with battle damage for TNG's "The Battle" and would have looked awkward up close in the new footage pre-battle, which was why it most likely wasn't used.
If they wanted a newer ship, they could have spotlighted the Nebula or even the Ambassador, both of which were present and correct in the scene. As was the Excelsior, the main cruiser/ship of the week seen in TNG.
I think they wanted a smaller (in-universe), more detailed ship for the closeup shots, and the Reliant model was the most detailed one they had that fit this bill.
The Miranda model works well for that story. I don't know how much thought went into the modifications, but removing the rollbar and substituting it for some nondescript scientific equipment makes the ship seem even weaker, and the presence of civilians underlines that they were never supposed to be in that situation.
I never really understood those modifications. I get removing the rollbar a la the Lantree, but adding those little protuberances on the sides that looked amazingly like guns to me (although they didn't actually fire) made the ship look more like a warship than a weaker vessel.
If they had unlimited money, maybe there was an opening for a small TNG era ship, perhaps based on one of the Wolf 359 kitbashes. But I bet they wouldn't have wanted to use any Galaxy components. The New Orleans would have seemed too similar to the Enterprise-D.
As I mentioned earlier, I would have gone with the minimalist approach: Just a saucer and one nacelle like the Franz Joseph Saladin/Hermes class (but maybe more contemporary to the era) so that the three pyro models would have had less build time and less materials.
It's interesting to speculate what a totally new Starfleet ship would have looked like in 1992. Would it have been anything like the dart direction Voyager took? Or maybe one of the Nova concepts from the TNG TM?
That's a good question. I would say no to the dart look. That didn't start until John Eaves designed the Enterprise-E. I definitely think an elliptical saucer like the Ent-D's would have been the norm, but I think they would have made the overall ship smaller in scale (which was the original plan for the Nebula class Phoenix) and would have gone the route of either the Cheyenne or the Challenger, as nobody would mistake either of those designs for the Galaxy class.
But yes, another direction would have been to base the ship off of one of the designs from the tech manual, as that book had been published in 1991. But those designs weren't hugely fleshed out.
Incidentally, they were thinking of building a new model for the USS Raman in the 7th season TNG episode "Interface" (although that would have been a year after 'Emissary.') Would it have been a TNG version of the Oberth?
The more I think about this, the more I think that it wasn't really necessary for them to come up with a new design/model for the Saratoga. The nature of DS9 meant that they wouldn't be around Starfleet all that much, so seeing starships would have been few and far between. Past Emissary, the only guest starships we saw were the Nebula class Prometheus (stock footage of which was used for other ships), the Galaxy class Odyssey and Venture, and the refit Excelsior class Lakota, before new models were built for Voyager such as the Intrepid class and the Greg Jein Excelsior for 'Flashback,' both of which were used in later episodes of DS9.