FJ
Can you let us know which airport and which approach please? It would help to see a picture.
"Maneuvering space" is not a meaningful term for procedures. You either fly the published procedure from an IAF, or you are radar vectored on to the LLZ for the approach. There's nothing to stop you suggesting headings to the controller, however, which may end up being the equivalent.
What I don't follow is why your self-positioning manoeuvre was more expedient than getting radar vectors for the approach in the first place.