I hear you on the stability front-shooting 12" targets past 300 yards with the long legs definitely pushes the limits of an ultralight system.
The main reason you're likely struggling compared to a traditional setup is that the Javelin Lite uses a magnetic 'hold-open' system. It’s great for saving weight, but it doesn't provide a rigid lock. For those longer shots, you really want to look at the Pro Hunt Tac head.
Unlike the Lite, the Tac head has a mechanical locking gate. Once those legs are clicked into place, they are physically locked open. This creates a much more rigid frame that doesn't 'give' when you load the bipod or under recoil. It effectively turns that long-legged setup into a rock-solid tripod when paired with your pack as a rear rest.
If you're hunting for precision at distance rather than just counting every ounce, the mechanical lock on the Tac head is the game-changer for that 'locked-in' feel you're currently missing