Tube sealant vs. tire liners vs. puncture-resistant tires -- which best prevents flats?
There is more to tire set-up than just puncture proof.  Many are also interested in tire suppleness, traction and rolling resistance. Tubeless tires are the in thing at the moment because tubeless construction take material away (aka the the tube) and allows lower pressures, which results in a more supple tire, that has more traction and often less rolling resistance.  

Supple tires can often roll faster and with less effort as they deform more easily to surface imperfections. This translates into a smoother ride and less pedaling effort and more traction. Many of the puncture proof setups add material to the tire making the tire carcass stiffer, this in turns means it takes more energy to deform the tire when rolling (or encountering a bump), which in turns results in a harsher ride and a higher rolling resistance (the energy to deform the tire has to come from somewhere; i.e., forward momentum).

Summarizing:


Tire Liner - Cheap and reusable as it can be applied to current tires, but has a fiddly set up (e.g., getting the liner to stay in place), will reduce suppleness of the tire and does not provide puncture protection on the side wall.
Puncture resistant tires - These have what is in essence a liner built into the tire carcass. Because of the unified construction should be more supple build than a tire liner and vary the degree of coverage. Different manufacturers and models will have different trade-off between suppleness and puncture resistance.
Tubeless - Primary goal is really to create a lighter, more supple tire, that can be run at lower pressures, the setup also happens to have good puncture resistance properties if sealant levels are maintained. Mounting a tubeless setup can be a hassle (i.e., you need high pressure to seat the tire), sealant is required and handles sealing the system including handling punctures. Sealant also needs to be topped up every few months as it dries out, and without sealant you lose puncture protection. The setup also requires wheels with tubeless compatible or tubeless ready rims, tubeless tape, and tubeless valves are also required. The design goal was less to be "better" than (1) or (2) in terms of puncture protection, but optimizing the tire for a different set of criteria (i.e., weight, suppleness, traction, rolling resistance and puncture protection).


If puncture resistance is your only concern then your "double-shield" setup looks like a good solution and will be easier than tubeless.