No? I mean, you make a lot of cores.
Ok, the most primitive model:
You have X big cores. Each core separately is capable of powering an FTL field. You use core 1 and monitor the charge; the current hitting it is A. When the charge gets worrisome, you switch to core 2. At the same time you start bombarding the 1st core with the positive current of A/(X-1). Then you switch to core 3, etc. By the time you cycle back to core 1 it's completely free of charge.
That's a very primitive scheme. In actuality you do it with lots and lots of small, unevenly tasked cores, so not only the switch between them is smooth and doesn't drop you out of FTL, but the total amount of them is somewhat lower, and the neutralization is more efficient.
Yes, this is expensive, the total amount of eezo used is several times higher than it would be otherwise. For unlimited FTL it's worth it.