Well Nepleslian, NDI, and Yamatain definitions for heavy and light cruiser differ somewhat.
The C3a has about the same internal space as a DD4 or C1 though its sectioned very differently for much less crew space and much more equipment. These ships are considered destroyer and a cruiser respectively. This is largely because Nepleslians view ships as needing to be big, and the NDI view them as needing to be really REALLY big. The closest thing Yamatai has to these ships I estimated to be the Eikan heavy cruiser.
Eikan:
https://wiki.stararmy.com/doku.php?id=st ... vy_cruiser
DD4:
https://wiki.stararmy.com/doku.php?id=dd4-d
Here is how I got my estimates:
The DD4 is almost always described as a big brick of manliness so I estimate its internal volume to be like a brick, Height x Length X Width or 170 x 156.6 x 25 for an internal volume of ~665,550 Though the actual space is certainly much less than this.
The Eikan is hard to estimate because of all the pokey bits on it but here is how I estimated its internal volume. I couldn't really tell how far the wings poke out relative to the body so I guessed they about double the height and width of the ship and don't contribute heavily to the internal volume. The ship also has a wedge shape so I viewed that as a triangle from the top and sides (halving and halving again) There are also lots more indention, protrusions, and other bits but I think those will more or less even out so long as the big swaths of empty space covered under the dimensions of the ship are removed.
That left me with (365 x (1/2)160 x (1/2)367.5) x (1/4) ~= 408800 though the actual space would be a bit less than this.
And the C3 is simple, its length and height are almost entirely filled with stuff, just the width needs to be halved to accommodate for the radiator wings.
This got me: 328 x (1/2)75 x 26.7 ~= 328410 though actual space would be a bit less than this.
Which puts all of these ships roughly in the same category for size. The c3 also has a very solid build because it doesn't use weird geometry and when armored I think would easily compare to ships the size of the Eikan (though perhaps not the DD4, which is really just a massively armored space brick).
Edit: In terms of the system scaling up the next rank of battleship would be held by the Chiharu class which I assumed had a similar shape to the Eikan which would give it an internal volume of ~375,000,000 and the Plumbera (two ranks down) would only have ~67733.
More Edit: Added another armor/shield/mitigation rating of 20/20/2 for the unarmored version.
Even more Edit: Decided to reduce the armor from 40/40/4 to 30/30/3
Even more, more edits: Further elaborated on the DR rating for the ship. If This is still confusing some people I'll dumb it down further but I don't think it will be an issue. Also decided that additional FTL features could be better done as separate entries later so the ship's FTL system has been changed down to only what has been pre-approved in other entrys.