Currently on Holodeck, I am unable to modify whatever starship my characters were using before the launch of Legacy of Romulus, due to an inexplicable 750 Zen fee. Switching ships indicates that it's only on whatever ship the character was in at the launch of LoR, and it seems to be the same bug as was reported on Tribble: that the Exeter is muscling itself into Fed and KDF customization!
I don't mind the Exeter, but I don't own it and likely never will since it doesn't have a Tier 5 counterpart. Requiring me to own it to customize ships that have nothing to do with it is a nonsensical, unfair, and irritating bug.
In case you or someone else are still having problems with this, I was able to resolve it for my Constitution Cruiser by clicking Randomize until the Zen cost went away and customizing my ship from there.