Go back to your orthodontist and tell them you would like to get it fixed better. Most orthodontists will want you to be happy with the results of your treatment and will try to help you if you are not happy.
DON'T do lumineers, Go to a good orthodontic specialist, tell him exactly what your problem is, exactly how much time you have, use fixed braces (clear if you want them) from a real orthodontist and have him do everything he can as fast as he can. I am an orthodontist have seen this problem often. We can almost always work out a way to get you to your wedding looking great . If the problem is really severe I have even done as much as we can before wedding, take the braces off, go get married and then come back later after wedding and finish up if we have to. We want you looking and feeling great at your wedding.
I just saw another posterior open bite from Invisalign last week. Patient is very unhappy with situation and seems to be contacting mainly just on upper left second molar. Another office did the treatment for a front tooth that was displaced in a softball accident. The treatment apparently did not work entirely well, got rather long with more aligners, and now patient has a posterior open bite and can not chew properly. I took a cone beam CT scan and bite is clearly open in front and back. The condyles look OK with reduced joint space left. Don't know how long it has been that way. I suggested it may be possible posterior intrusion or a possible change of jaw/bite position due to lost neurologic sense of where to bite (engram) ?? I suggested that she stop wearing aligners and try to give teeth time to re-erupt and/or for the bite to adapt but patient is seeking other opinions also. I would not recommend crowns as time and adaptive capacity might be able to improve the situation, I would at least try that before other interventions.
My opinion is that veneers to fix a problem like this would be an absolutely terrible idea. As an orthodontist I have had to go in and try to fix messes like that afterward when it doesn't work well and doesn't really look good, We had to take off all the veneers, try to find out where the roots were located, then reposition the roots where they were supposed to be in the first place. To do that we had to put temporaries on, put on braces to straighten out the teeth so that a good restorative dentist could put decent crowns or veneers back on to replace all of the enamel that should have never been cut off of the teeth in the first place. My opinion is don't waste your time with aligners with this one. Get some braces on, straighten the teeth out and get it over with. I could have those front teeth looking a LOT better in 3 to 4 months. This should not take "years" to do this even with excellent orthodontic refinement after the initial 3 to 4 months of initial alignment. Sorry if I sound a bit judgmental but I really hate to see patients go through all this when we could have just straightened the teeth very easily and had a perfect undamaged set of teeth with no crowns or veneers at all. In addition they probably spent several times what it would cost to just do it right to begin with.
Your question surprises me a bit. If you have unerupted permanent cuspids didn't anyone talk to you about having them uncovered and brought into position where they should be?? Is the person doing your Invisalign treatment an orthodontic specialist or a dentist who "does orthodontics" without any specialty training? As an orthodontic specialiist the first discussion I would have with you is about bringing the impacted cuspids into their proper positions. It can't always be done but that is the first thing I would consider. What is the plan for the unexposed teeth after the Invisalign? A cone beam CT scan would help to determine the exact positions of the unerupted cuspids and help to see what it would take to move them into position.