Okay, so the DUST game has yet (after 2+ years of development) to add in the original purpose of the game. That purpose is for EVE pilots to CONTRACT the DUST Mercs to take specific Districts for them to use. Without a clear and definite goal, all the rest doesn't matter. Why control a district? Passive income, that is being found to be a bad thing now.
Honestly Mercs should not be producing income, they should not be receiving passive income (unless it's from a form of defense contract), and they should not be as short on cash as they are now.
What should be happening is that EVE players should WANT DUST players to take and hold districts for them. The EVE players should want it so much that they would be willing to pay hundreds of millions of ISK to get that district. Whether that happen by usage of a Warbarge and escort fleet or by shear ISK contracting, the EVE players need a REASON to want the DUST players to take that district.
So we need for you to give the EVE players a reason to want to own access to a district! Something where the EVE pilots can get some needed resource from districts that can be gotten no other way. Then this resource can be used to build other things like dropsuits, weapons, or vehicles for DUST or even implants and other things for EVE. Then the EVE players will start fighting one another for control of the new resources. This generates content not only for EVE, but for DUST as well.
It's such a simple thing to do, and it will add so much to both games.
So basically you need to add in a contracting system where an EVE pilot/corp/alliance can setup a contract for a DUST merc/corp/alliance to fulfill. Use the system you already have in the EVE game. Next you need to have Planetary Interaction or something similar to that start generating these new resources. Or maybe you don't have to add in any new resources. Maybe the only way to generate the current PI resources is by controlling the district? Maybe in highsec, PI resource generation is available because it's run by the different factions and they want the economy to continue, but in low-sec and null-sec only the group that controls the district is allowed to do any PI in that district.
Anyways, this creates a reason for EVE players to want to hire DUST players to take control of districts for them. Once you get this done, then it paves the way for the next step which is combining the markets of both games. I detail that idea here:
https://forums.dust514.com/default.aspx?g=posts&t=154688