At some point after you contact approach, you'll get an instruction to maintain heading X and expect vectors for runway Z. If I remember correctly, "request instrument approach" and "cleared to final at pilot's discretion" will work after that point.
FYI, PFE interprets "request instrument approach" to mean that you want an ILS runway. If there is no ILS runway, your request will be denied. If there is an ILS runway, you'll get vectors to it. If you want to fly a full IAP, use "cleared to final at pilot's discretion" instead and you'll get no further instructions until you're established on final and contact tower.