1. Traveller as a reflection of current events
Generally, role playing can be used as an escape from reality, a metaphor for it, or a way to work it out virtually.
The Solomani Confederation could be a future successor to Nazi Germany, Soviet Russia or Communist China. They can't be the antagonists of the Honorverse, Haven, since they don't have the overwhelming numbers of capital ships, nor is the Imperium the underdog.
However, you probably do have a factionalized ruling party, with an expansionist policy, and an apolitical military that needs both to be monitored and mollified by turns.
The Solomani resent any form of containment, but may have found their Siberia in Rimward expansion, free of competing interests.
The Party may have given their commercial interests a more or less free hand to trade, allowing a rapid rise in revenue, which in turn gets partially channelled in increasing their military spending.
Despite having a single political apparatus steering the ship of state, politics in the Solomani Sphere tend to be fiercely local, heavily influenced by Terran history and traditions. I'll bet that part of about the right of the people bearing arms still can't be infringed.
The Imperium may actually be the New World, with Solomani immigrants viewing that their loyalty lies with their new homeland.
2. Spinward Solomani Sea
The Solomani have not given up the claim to the space they believe belongs to them, currently administered by the Imeprium or their puppet states. An aggressive policy to slowing re-exerting hegemony over these disputed areas and rebel provinces is starting to make itself be felt.
3. Solomani Military
The Solomani military definitely know that they lag technologically behind the Imperium, but are willing to experiment with new doctrines and technological innovations in order to level the playing field. This includes importing TL15 equipment, dual use if a military embargo is in place.
4. Minimum fleet specifications
I'm going to base it around Jump 3, because their lines of communication are shorter than the Imperium's. Their flying squadrons would be Jump 4 and their deep strike ones would be Jump 5.
5. Troop Transports
A Marine division of 8400 souls sounds a little short, and does bring into question how a totalitarian government plans to keep five plus sectors worth of worlds suppressed. I suppose that ordinary army units are levied and that their home planets are responsible for their transports. Or they go Imperial Guard on them, and use them up, which means transport is the Navy's problem.