I agree with Paarker. The visible glue line is only one of your problems. Gluing a support board across the grain could present a problem if there was any movement issues.
Assuming you don't want to cut them apart, any fill in the grooves would be an obvious fix. You could use a "V" joint router bit and run a shallow pass to create a cleaner line. If nothing else, use a small artists brush and a paint that would be compatible with your topcoats, and paint out the glue line.