Ok. First off thinking about it, I really like most of the aspects of the current "warp" system, and it's due to gameplay implications I think it needs to be changed a little.
It's great that it doesn't remove you from the world. That's also the main reason "warp" isn't a fitting name. It uses the same Newtonian physics as normally flying arround in the prototype, this underlines that it really is the same space and physics.
I think the philosophy of using it should change from Activate/Deactivate to Single Burst Burns. Everything else is actually pretty good.
What the "warp" drive actually does is switch you to flight assist mode, take controll of lateral trust away from you and increase max acceleration of all engines to insane numbers, yes all, not just the front and back ones and that's ok if the interface, the phylosophy changes.
My proposial is to make it simmilar to the boost button. You have to hold it for "warp" to engage and stay active. If you release it the ship returns to normal operation. Also limit it's use. Maybe allow to enter it in both Flight Assist on and off modes. In On mode it would act like it does now. In off mode you can directly controll the "super acceleration" with your joystick axis or front back buttons.
This could have the drawback that, for balancing reason and enjoyment, the max "in warp" time could be more then twenty seconds. In that case I would stick with a toggle button to not anoy the player but still have it auto switch off after the max time/energy/fuel runs out.
This would encourage people to use it as it actually functions, more of an extension of the newtonian flight system then some totally different system.