Well your idea does have the charm of being somewhat based in Trek when we look at the IKS T'Ong from TNG:Emissary where a K't'inga was used for a long-range operation of some sort.
So they are useable for lon range investigative missions of some sort.
The model probelm was not actually existent at first.
At some point they reversed the low-quality and the high-quality model which are displayed at different viewing distances.
But since it is a problem that affects the Klingons there is no need to be bothered with fixing it.
Same ges for the still-missing aft Photon Torpedo tube which the K't'inga has had since 1978.
What exactly did you have in mind statwise?
Commander Science, LtC Engineering?
Or perhaps since the K't'inag is an old warhorse Commander Science with LtC Tactical?
In any case to be effective as a science ship it would be good if it had 4 Science consoles.
Perhaps a console and maneuverability layout siilar to the RSSV would work.
Meaning a little buff in agility over the T3 K't'inga similar to what I describe in my long-winded speech.
Howeve in both your and my case the K't'inga would not gain much hull.
But that is probably not that bad since it is lighter than a Nova.
I like the idea of a light cruiser, but I think that a cruisery science ship would fill a larger gap in the KDF's ship roster as there are three cruisers, but one science ship at T5.
As for the Neb's Bof layout, I believe it's Lt Tactical, Cmdr & Ens Sci, Lt Cmdr Eng, and Lt Universal, with two tac, two eng, and three sci consoles. I think if another sci were used as a base, the tactical edge the Luna has over the Intrepid or the Oracle's extra eng capablity would be more appropriate for the K'tinga, but I think the Nebula layout best fits it's whole "work horse" thing.