Dead Tooth and Flap Surgery

Hi, I have a two-fold issue that you might be able to help me with. 1. One of my front teeth died(one right next to my two upper front teeth) when I had braces a few years back. It is holding up very well and does not seem lose at all but I would like to get it repaired as soon as possible obviously. The tooth has a few horizontal cracks near the bottom which have been there for over 10 years and I was told by my current dentist that I would need a specialist to handle it. He gave me an estimate of about $900 to get a root canal and temporary filling but was not able to advise me on the price for a permanent solution. Can you give me an estimate on the additional work that would need to be done? It would have to involve something like internal bleaching and probably a porcelain cap. Is there any way to keep as much of my original tooth as possible and just cap the hole? I am located in south Florida for your price references. 2. There appears to be some type of debris leftover from when I had my braces embedded in my gums. Whenever flossing in the area(just this specific area) between my two top teeth next to my top molars I get bleeding and I feel like there is something inside that area. It has been this way since I got my braces put on but I was told that it was due to the metal around my teeth trapping food particles. When the braces were removed this problem persisted. I went to a dentist and got a debridement which did not solve the problem, also strangely, no evidence of calcification was found like a typical periodontal disease would cause. Instead, there was a large amount of dental cement found still under the gumline from when I had braces. I believe there is still some left, but within scar tissue embedded in my gums for the above reasons. This will probably require flap surgery to remove, but before I can do so I need some diagnostic tests. What would you recommend? I was considering a CT Scan with contrast which might reveal the problem areas. My main concern is that it might even be food particles or something similar and a CT scan will not pick it up. Thus far x-rays have not been able to spot anything. I also vaguely remember not keeping track of dental spacers I had prior to the application of my braces, and I believe it is possible that they went up into my gums before the procedure. All these things have to be considered when selecting a test and I would like to know my options. On a side note, I developed nasal polyps after getting braces. I certainly have noticed a correlation between flare ups in my nasal polyps and flare ups in my gums. Could infection in my gums be traveling up to my nasal cavities? Thank you very much!