What is my Best Bet to Treat my Tetracycline Stained Teeth?

In my opinion I would veneer your teeth, I have whitened many tetracylcine teeth with a procedure called KoR Whitening with terrific results but I think in your case placing veneers would be the better option. 

I feel that a veneer is the least invasive procedure.  By reducing the surface of the tooth appropriately, the porcelain can be made thick enough to mask the discoloration and retain the natural shape and appearance of the tooth.  I do not think Lumineers are a good choice, they are an inexpensive knock off of the traditional veneer and do not work well in your situation.

I would choose the veneer option

Good luck with whatever decision you make

Unlike foods and smoking which stain the surface of the teeth, tetracycline is absorbed into the tooth structure as it is forming anf growing.  It is an internal discoloration.  Tooth whitening will not succeed in masking this type of discoloration.  Plastic composite bonding can be used to hide the stains, but over time the composites will stain, margins break down and the restoration loose it's aesthetics.

I feel that a veneer is the least invasive procedure.  By reducing the surface of the tooth appropriately, the porcelain can be made thick enough to mask the discoloration and retain the natural shape and appearance of the tooth.  I do not think Lumineers are a good choice, they are an inexpensive knock off of the traditional veneer and do not work well in your situation.

Another alternative would be a crown.  Choosing between and veneer and crown would be dependent on whether there are significant dental restorations existing in these teeth already.