What I do is demolish the Equestrian Center, go into Edit Town mode and place the appropriate lot size for the Equestrian Center somewhere in the town and put the equestrian center there. On my game, it still won't let me move sims into the now empty lot (because there is no furniture, it won't let sims move in), so I just place a tissue box or something small and cheap like that in the lot. Then, it lets me move sims in the lot because it has furniture. After this, when playing the family I just sell the item and I have the required amount of money for starting legacies.
Since I have the Pets expansion pack, I have to do this to start legacies. You could also just do what you said, and place another 60x60 lot in the town.
(Sorry if this was unclear or late- if I need to, I’ll rewrite it so it makes more since. I hope this was helpful!)