In my opinion, the circle should be smaller, and the cap-speed faster for this mode in order to promote aggressive capping. By all means, due to how large the circles are, both teams could afford to stick close to island cover and wait each other out while camping.
My proposal would be rather than following standard cap rules, Epicenter should allow cappers to continue capping even if defenders step on it: In that, as long as the number of players in one team inside the zone is greater than the number of players on the enemy team, they would cap in multipliers based on the difference of ships between teams in that zone. If the area was captured in a 3v2 situation, even if the cap speed is only 1x, they would still only receive cap-assists.
4v1 ships inside the cap zone = 3x capping speed
3v2 ships inside the cap zone = 1x capping speed
Shooting any of these players would reset the cap partially, but ignoring a player completely will still get the zone captured.
4 cappers vs 3 defenders, 3 cappers get reset regularly = 1x capping speed, but due to having resets, capping speed is effectively 1/4 normal (240s to cap)
5 cappers vs 1 defender, 2 get reset regularly = 4x capping speed, but due to having resets, capping speed is effectively 2x normal (30s to cap)
To promote ships actually heading in, I propose even more options that may or may not be mixed together. Numbers are placeholders:
Increase the cap values - 3/tick outer ring, 6/tick inner ring & 9/tick epicenter
Smaller cap zone
Repair 1% ship HP every 5s in the center of the map (500s/8min 20s from 0 to 100% HP) - Excludes damaged/destroyed modules. Due to their significantly larger HP pools, Battleships would benefit the absolute most from this mechanic while destroyers get miniscule repair bonuses.
"King of the Hill" ribbons for attacking ships while inside the epicenter; +10% award modifier to hits (Ex. 1 shell damages enemy HP by 1%, normally, the reward will be 100 credits, but with this, it will be 110). Alternatively, this ribbon could be given out every 90 seconds that player stays inside the very center, it will have the same awards as cap assists, but be a different flag.
This suggestion would promote more ships heading inside the cap circles to 'outweigh' the enemy team because the current gameplay with the zone is still effectively campy