To promote the markets in the other Empires, install 1-way shipcasters in Jita that lead directly to the primary Amarr, Gallente and Minmatar trading hubs.
If you want to sell in Jita you still have to run the usual gauntlet, but once there you can load up and bypass everything with a single jump back.
Don’t shipcasters randomly deposit you in the exit system? If not, in theory - yeah, I guess you could camp both (but at the 0.9 security safety, and probably with more than a few CONCORD ships lurking about).
Make it so that you are required to have a special item in cargo hold to can use the shipcaster which is consumed in the process: Jita Outbound Hauling Permit.
I mean, why have use an Amarr market when you can buy the items in Jita and be teleported back to where you were?
I still believe that the way to have healthy independent markets besides Jita is not to increase connectivity but to decrease it. Cut HS apart into separate HS islands surrounded by LS and then add unique economical bonuses to produce faction-specific items in each of those regions, so that people get opportunities and thus reasons to use and stock those markets.
Unique Economical bonuses in each places would be nice. Agree Faction-specific items get cheaper taxes and such.
Make the taxes in the non faction 2x or 4x higher?
Jita →
Gallente in Jita 4x higher
Serpentis 1.5x (Due to opposite pirate faction of Caldari
All others 2x
Then just put a only 1 .5 between all of them that is the central warp point that links them.
You now risk moving your stuff between systems BUT same time you now get a benefit to go to the other trading hubs so you pay cheaper taxes. which would be a huge deduction.