While I am not a manager, may I highlight a couple of things.

Firstly, may I point out Unlimited Projection was a fairly unique ship, and it seems unlikely one would be deployed to set up shop as a factory on a new world? Indeed it would be an incredibly poor choice for such a task.

For example it would make more sense to have one of the Lucrehulks be loaded with materials to build a factory? Indeed there is abundant hull space to fit a prefabricated factory.

Secondly, there is no indication the Unlimited Projection could dock with a ring to become a full battleship. Indeed it lacks the prominent bridges which form part of the connection to the rim.

Now if we take a look at both ships side by side, we are able to see the front of both ships, marked by the front facing dish (red arrows).

Also, if we examine the bridge and connecting assembly (which links into the rim) is present in the standard model (blue) but not the Unlimited Projection (green).

This seems to be because the Unlimited Projection was a purpose built factory vessel used for support of military operations (much as repair ships are used in real fleets) and for communications (note the extensive comms aerials) but seemingly is armed and armoured scantily in comparison to a normal lucrehulk core ship.

Indeed this would appear to fit the combat doctrine of the Seperatists, because the Lucrehulk-class Battleship was a major line ship, and it would make little sense to deploy a factory/comms vessel with an expensive rim which was adorned with hundreds of weapons which would leave a proper core ship (with full weapons and armour) unable to function as a full ship of the line.

A very crude comparison might be an aircraft carrier, we do not fit them with heavy cannons (such as 12 inch guns) for engaging other ships, as that is not part of their combat role.

Now if the rim had been ghetto rigged on at the end of the clone wars, with people making do with what was available this might make more sense, but this wouldn't fit your plot as it presently is.

Thirdly (and finally!) "dropping" the rim would be unlikely with any precision, I've seen little evidence that a lucrehulk's rim has atmospheric manouvering thrusters (and it would be likely almost impossible to manouvre a 3km wide ship with any degree of accuracy anyway.

Equally, there is little evidence a Lucrehulk rim can manouvre independently at all, as all command and control systems appear to be in the core. Now it might be possible to reroute some controls to the engine room or something, but hardly to the extent of being able to thread a needle with such perfect precision as this.

Now, another point to be raised is that if it has no atmospheric thrusters to slow its descent, why it does not simply crumple and tear itself apart (indeed there is a vulnerable section of superstructure exposed by the removal of the core ship which is clearly open to this). If you consider the relative velocities and weights (I'm not doing the maths today!) involved, the lucrehulk would likely cause an extinction level event (even if it was intact which seems unlikely) when it made its massive impact on the planet.

Returning to the point of the fine precision needed by "dropping" the ring around the core, consider the neck which protrudes from the rear of the lucrehulk rim (intended to connect to the core), this bit protruding out of the middle would really add another degree of impossibility to the whole ridiculous affair, not only is it like threading a needle, but its like threading a needle where you are not allowed to have the thread touch the eye of the needle...

Thus I would propose a more sensible measure.

1x CIS Factory which had been loaded aboard the empty space inside your Lucrehulk-class ship (likely not a front line model at any rate (and so likely has much empty hangar space usually occupied by landing ships/mtts etc), why would they deploy a front-line battleship (or indeed a pair of them) as such a desperate stage in the Clone Wars on a mission to open a factory which at this stage would have no impact on the outcome of the war).
1x Mk1 Packed Earth Wall maybe even a Stone Wall possibly a Trench System!

Think how many choices you have for this, without going in for swanky modified ships or battleships being sent out to garrison an unpopulated world (why couldn't a pair of freighters with a corvette in escort perform the same operation, all the while attracting much less Republic attention and strengthening the CIS line fleet against its New Republic Adversaries), you could instead have a flavourful and more realistic Seperatist Holdout!