I think that 単の (and by extension ただ単の) is an unusual expression. 単に and ただ単に are regularly used. That's an adverbial form, so you won't use it with a noun sentence, but here you can easily make it into a verb sentence with リハーサルをした
ただ単にリハーサルをしたので、今日は本気に演奏します
or you can keep your original structure and just go with ただのリハーサル
The reason/cause precedes ので and the result follows it, so that Japanese sentence sounds awkward (understandable enough, though). Also, it's necessary to make more clear that the rehearsal was done before.