I am not playing that frequently to experience all situations in core, but if problem is that players prefer to stay safe, within relatively low risk and constant profit, only thing possibly influencing their decision to go to core is potentialy high profit for significantly higher risk. Maybe this motive will make you think about it:
Assignments representation
Lets say a wheat farmer is taking care of his field for average daily profit of 400 currency units. Risk is low and even if weather and season arent hospitable one year, another year it will be better. So average profit over few year aswell as minimum salary every year is guaranteed.
Solo Core Runs representation
Lets say farmer got an opportunity to travel to another country, where industry is more expanding but chance to employ is 50%. Average income for worker there is 1000 currency units.
Now lets compare both, 1st option is providing low but stable income of 400. While another option is rewarding in average 50% * 1000 = 500. Which option would you choose? For every poor yokel, first option is the only choice. Nobody would exchange 50% chance to loose his living for 25% higher income.
In terms of game, core has to be rewarding much more to motivate all kind of players venture inside.
Problems
1. Most of the ZC fighters will do much better accomplishing 1 SS mission than doing ZC for 1 hour( not taking into account loot from players, just ZC reward, I assumed, over long time, player loose as much gear as he gains)
2. Running dungeon(s) is dumb and dump of your sources. Only valuable stuff there are modules, well maybe 2 or 3 oil cans... But nothing else worth going there, in average its realy money dump.
3. Looting polymer lab is REALY nice, i love it always, but i am not sure if any other zone is as profitable to loot, in general you ll die more and loose more of your time than just running assignments and buying polymers, kevlars...whatever.
Solution for ZC
1a. Pay 50-100 caps Fix Reward for every single character active in zone since begining till the end of timer.
1b. ZC Ammo Reward, Repay 20% of base cost of ammunition for loosing teams and 50% for winner.
1c. Boost ZC Score reward by 20-30%
1d. Reward for supportive characters, reward is given to everyone who use fa/stim/ss/doc/defib on friendly player. Total reward should be capped per each player dependent of his ZC score. E.g. Miniguner deals 1000 damage, medic heals 500 hp in process. Medic earns additional 50% amount of miniguners score. If he would heal Miniguner for 1500 hp, he would not get more than just 100% of score anyway.
Solution for Dungeon(s)
2a. Add more!
2b. Boost XP reward
2c. Instanced Treasures!!! CAPS, MKIII ARMORS, ROCKET LAUNCHERS...
Solution for loot spawning in core
3a. More characteristic spawns, so one can acutaly learn where to find desired resource. It works quite nice in polymer lab, but other seems to be inapproprate( for me)
3b. More loot
Thats it