Starfleet probably ordered all Federation ships in the vicinity to attack the Borg with all they've got, including prototypes, civilians, non-Starfleeters, etc.

Here are my ideas:
Enterprise/Const. Study Model ->
An old vessel, probably not Starfleet, but from a native Federation 'Navy'(Vulcan?) nearby.

Excelsior SM's
Real Starfleet classes, except maybe for the 4-naceller. Maybe one of them is the Hokule'a Class?

Nebula SM's
The four naceller is probably a pretty standard Nebbie with w couple of NO-nacelles in place of the Sensor Pod.
The weird thing with the cut-off nacelles is possibly some kind of prototype. At least it's a one-of-a-kind ship.

Any other theories? (Bernd, Timo?)

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Prakesh's Star Trek Site

The pre-Phase II triangular-hull ships could be much older ships, perhaps very large ones (some fan sources suggest fightercarriers) so that they might survive and be of some use in the TNG era - or then very small local patrol vessels. I can't think of any canonical class that would be suited for them.

I'd consider the extra nacelles on the Nebula models minor variations that would not necessitate a new class name. However, the secondary hulls of those ships are Galaxy-like, not shortened and rounded as in the definite Nebulas, and I consider THAT as a sufficient basis for considering these ships (and the various tabletop ships based on these models) as members of another subclass if not another class. This could even be the elusive Rigel class (with high-60000 registries) for which no real model exists.

They were both exclusively constructed from Galaxy parts (1/1400 plus 1/2500 "New Orleans size" nacelles). The small nacelles are attached to the rear end of the saucer with probably custom-made pylons. The engineering hull is about in the same location as on the final Nebula, only the shape is still completely Galaxy (so it would be a heavily modified Nebula). One model was severely damaged and clearly labeled "USS Melbourne NCC-62043". This is definitely the ship at Wolf 359: http://www.uni-siegen.de/~ihe/bs/startrek/articles/wolf359/rigel-screen2.jpg
(This is a 100% certain confirmation!)

The nacelles are not, as one might suppose, mounted to the very rear end of the secondary hull, but to the saucer as mentioned above. They are about where the pod is attached in the later versions of the Nebula.

The other one (from Riker's ready room in "Future Imperfect" is probably labeled "Melbourne" too. I suppose it's very similar, if not identical to the destroyed model.

So with renewed vigor, I'd call the BoBW design a separate class altogether! The fact that the saucer is similar to a Nebula saucer doesn't mean much, since it's also similar to a Galaxy. And the New Orleans and the Springfield also have near-identical saucers.

The small extra nacelles wouldn't be a permanent fixture of this separate class, though, since we have seen different module arrangements in "The Wounded" and in Sisko's tabletop model.

If we call the BoBW design the Rigel class, we're rather well off: USS Tolstoy is then on screen in the "Shelby scene" (and the Excelsior class Melbourne could be the big wrecked saucer in the forefront, so all the ships mentioned could be on screen there). The registry range of Rigels would match the design. And the specific registry of the Tolstoy is almost identical to that of the Melbourne - Bernd, do you know how much of the rego survived when the "battle damage" was applied? We could thus get out of the "two-Melbourne trap", too.