The problems with low sec
Lack of a unique resource
Low number of people
Non profitable for corporations
2 different, non relate, crowds using the same space (FW and Pirates)
My solution is to expand the FW to include the pirate factions that we have in-game. Players will be allowed to join Sanshas, Blood Raiders, etc... And this factions will fight for the control of systems in LS.
Here come in play the unique new resource: the possibility of building pirate and special issues ships. FW have access to unique ship through loyalty points, same for pirate ships that can be bought in LP stores. So why don’t give the players the possibility of buying BPC with 10 runs for example, instead of build ships, and make only possible to build this ships in conquered systems in LS? This ships could be built in specials structures that would be produced by PI, and they would be invulnerable until the system change control to another faction.
This would encourage pirates to bring and protect systems so industrialists and miners could build this ships, mission runners to collect the loyalty points to buy BPC, which would increase traffic and number of targets for rival factions and solo pirates.
Now you have the umbrella to increase the production of whatever you want. Boosters, black codes, you name it. Just link them with this concept of sovereignty, and you will have all the goods that you need to smuggle to hi sec.
The FW already have a mechanism to control territory in LS, needs fixing, but its there, and is a system much more dynamic then null sec sov warfare.
This solution bring something for every game stile in EVE. Industrialist, pirate, PI, miners, mission runners, but more important, brings profit and a unique activity to low sec. At same time, it would multiply the number of targets, encourage small gang pvp, link the in-game pirates with the pirate factions of the game’s lore, the profits wouldn't be good enough to bring null sec alliances to play, etc...
This solve all the problems that I mention: bring a unique resource: production of pirate and fleet issues ships, potentially increase the number of people by increase activities, bring profit to corps, sell of ships and other goods, and put together everybody in LS to play the same game. This also increase the need for capital ships, that will be needed when your corp decide to join a null sec alliance. ;-)
P.S. be kind, English is not my first language, and this is just a sketch, I can complement based on the comments.