He said specifically that it's consuming code space.

Note that the 8051 knows nothing about RAM and ROM - all it knows is CODE (ie, memory accessed by MOVC) and XDATA (ie, memory accessed by MOVX).
My suggestion was a way to move these constants from CODE space to XDATA space, while still remaining in ROM


No.
He is trying to reduce the size of the CODE footprint - CODE and ROM are not synonymous!

PS
You need to have a very clear understanding of this when working with the Triscend E5, as the fully-configurable Mappers allow you to map RAM, ROM, and goodness knows what else into the 8032's CODE and XDATA spaces entirely arbitrarily!
Now that can get really confusing!!