No, those ROM's can't usually be repaired/re-programmed. I think there were actually a few versions around, but I don't recall any legal ROMs being programmed into erasable chips.
I know of 2 common types of erasable PROMs, the UV windowed type, requiring exposure to appropriate lamps for erasure, and electrically erasable.
As a (presumably) legal owner of the ROMs, you could probably burn a couple of backup pairs, using your kick.rom file.
I'm not sure how you would go getting a blank replacement part, but I think it should be possible.
There is a number of hobby eprom programmer designs around, ranging in features, complexity, cost and ease of use. SiliconChip designed a kit, which may be available to you somewhere. Additionally, a number of business commonly program PROMs, so you may be able to pay for a one off service.