I just had another thought... the parking could be in the shuttle bay, in the back of the lower fuselage, jutting out of the slope of the hill. You could then take a "turbolift" up to the saucer section, where the rooms would be.

And I've always thought one of those mid-90s Chevy Luminas would be an ideal base to modify to make look like a shuttlecraft.

EDIT: yeah, kinda like this https://mikeshouts.com/minivan-turned-into-star-trek-shuttle... (though they used a Ford Aerostar)