Revision Rhinoplasty - Lengthened and Less Nostril Show

Compared to dorsal hump reduction, tip counter-rotation and reducing alar retraction are certainly technically more involved maneuvers.  Even though they involve more surgery than dorsal hump reduction, for a revision rhinoplasty specialist these are very commonly encountered issues.   

It is extremely difficult to answer your questions without seeing your photos or examining you  - the changes you speak of are possible with revision surgery

Without good before and after photographs, it is difficult to give you specific advice related to your nose. That being said, I agree with the other surgeons that is best to wait about one year before revising your nose.  However, I would still start the consultation process at the 6 month point. This gives you time to plan, consult with other doctors and educate yourself about rhinoplasty revision surgery.   I recommend consultations with at least 2 or 3 Board Certified Plastic Surgeons, since lengthening the nose and reducing nostril show are some of the more difficult techniques in rhinoplasty.

You've had alot done to your nose. Removing the radix graft and shaving down the dorsum should be a relatively straightforward procedure. Treating the tip is more complex and you should wait for the tissue planes are more defined in the range of 1 year. You may require grafts from the ear.

Revision rhinoplasty is one of the most difficult operations to do in the entire field of plastic surgery. Make sure that your surgeon has performed thousands of rhinoplasties before embarking on difficult revision rhinoplasty.
There are many different techniques that will reduce nostril show, some of which include trimming the membranous septal cartilage columella, and/or composite grafts taken from the ear to bring the nostril rim down. Also, cartilaginous grafts can be placed along the bridge to lessen an over-rotated nose. Full transfixion incision during a closed rhinoplasty technique will also deproject the tip of the nose and in fact derotate the tip. Extended spread grafts also are used to lengthen the nose and push the nose downward.
 

The lengthening of the nose and less show of the nostrils are very difficult problems to repair, they need an experienced plastic surgeon.

Have another consult by a Board certified plastic Surgeon and decide. Even if you have to pay for a full rhinoplasty again

You certainly can have a revision but I would wait at least a year before undergoing revision.  If you are unhappy with your doctor, seek another consult with someone else.

Let me assure you that your nose can be improved if the  surgery is done by a surgeon experienced in revision rhinoplasty. However be patient and wait 9-12 months after the original operation. If you're uncomfortable with the recommendations of your surgeon, get a second opinion.