Originally no, and iirc in the earlier refits (I.e. prior to the Enterprise A) it was still a horizontal core (or at least mostly so, there's some sort of vertical element but we see the horizontal core when Scotty's nephew goes to try and rescue his fellow engineering cadets as the emergency bulkhead descends), it's only later it became vertical.With two compatibility votes, we can only take one of these next two options and retain refit capabilities.
Vertical orientation seems like the more forward thinking option, but on the other hand we've had problems with the injectors before.
Did the connies have vertical cores?
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[X] Vertical Core (Size Reduction) (Compatible -> Refit)
Whilst I'm still a bit shaky on it (not knowing the next option we could go for) the advantages of a vertical core seem to be too great given we know nacelle and secondary hull length is probably gonna balloon up in the future.