This is a very good question and I come across this dilemma several times a week. It is hard to say from the photo if your tooth is restorable, but from my experience, even if you could save this tooth, it may not last that long as the foundation is very weak and this molar tooth is under a lot of biting forces as well. The most cost effective treatment with the longest lasting result is placing a dental implant in the area of this broken tooth. Implants have a great success track and last a long time with proper care and maintenance. I hope this helped.
I would try one more time bonding it and making sure the bite is correct and not causing any interference with the bonding in all chewing positions. If not, another viable option is placing a porcelain veneer on the tooth. That would give you the best esthetic result.
Root canals is an ideal treatment for saving your tooth. Once the root canal is done, the infected tooth should start feeling better within a few days. Most likely your dentist will make a small hole through your anchor tooth to perform the root canal and once root canal is complete, the small hole will be sealed with a permanent filling material. Just remember that sometimes it is possible for the porcelain of the anchor tooth to crack or break off, in which case a new bridge may be needed.
You would be a good candidate to align your teeth using Invisalign. You need to wear the aligners for 22 hours per day. I always advise my patients to be honest with themselves. If your life style does not allow you to wear the aligners the appropriate amount of time, you may want to consider traditional braces; however I find most people are very compliant with their aligners. You will love the result.
I think that you are an excellent candidate for Invisalign express case. It will only take 5-6 months with 10 trays.