Honestly, I think Tower Shield Specialist is great defensively but it seems to lack too much oomph offensively.
I personally prefer no archetype. You keep Weapon Training, which opens up all the wonderful Advanced Weapon Training options.
You lose the ability to change shield facing as an immediate action and you lose out on high ass touch AC, but I believe that the increase damage output is worth it.
I'd second that you should definitely keep weapon training. That tower shield combined with a good suit of armor will give you great AC, so you're more concerned with damage to avoid becoming too passive.
I'd suggest taking the Eldritch Guardian archetype. Get a tiny improved familiar, give them a tower shield as well, and take the Shield Wall feat. Your familiar can give you total cover and a +2 AC bonus while you go about your daily fightery life.
I love it, and it's not like the familiar is going to be attacking anything so the non-proficiency penalty doesn't matter :-P
Most of what I'm worried about is biting the -2 to hit while wielding the shield. That's worth two levels of weapon training, so it would take about 9 levels to overcome, and only provides a Weapon Specialization's worth more of damage. I'm not sure if the game is going to last that long, and I'm certain it won't go past 12th level.
It also allows you to get Advanced Weapon Training options (which are beastly good) and it enables you to use Gloves of Dueling (which are stupid good).
Shield Specialization is pretty great. Greater Shield Focus and Greater Shield Specialization are pretty crummy I think.
Not a huge fan of Missile/Ray Shield. Instead, if you have access to Weapon Training, you can get the Combat Reflexes + Cut from the Air + Spellcut + Smash from the Air combo. It provides a ton of extra defense as long as you have a good DEX, which you should have.
If you have Weapon Training, you should also look into the following advanced weapon trainings: Armed Bravery, Fighter's Reflexes, Versatile Training, Focus Weapon. All of them provide a scaling bonus to each of your weaknesses: Reflex saves, Will saves, skill points and damage. Of course, the previous combo and this combo are incompatible with the listed archetypes, so keep that in mind.
Wait around for the Armor Master's Handbook before trying this out. There really isn't anything in the game currently that makes a tower shield worth using, but you can certainly expect it to get some love in that book.
Is Covering Shield worth it more than Fighter's Reflexes?
In my opinion, not necessarily. Covering Shield is +5 or +6 to some reflex saves, while Fighter's Reflexes is ideally +5 when you get it (level 13th, while using Gloves of Dueling), and applies to all Reflex saves.
But you are free to take both, really.
Here's how I'd build my vanilla Tower Shield Fighter:
Human
Defender of the Society + Wary > Perception
S16+2 D15 C14 I10 W12 CH7
LV1. Shield Focus, Iron Will, Additional Traits > Indomitable Faith, Bruising Intellect
LV2. Weapon Focus (Heavy Pick)
LV3. Power Attack
LV4. Shield Specialization, +1 DEX
LV5. Weapon Training > Axes, Advanced Weapon Training > Versatile Training > Axes > Intimidate, Survival
LV6. Weapon Specialization (Heavy Pick)
LV7. Cut from the Air
LV8. Improved Critical (Heavy Pick), +1 STR
LV9. Weapon Training > Advanced Weapon Training > Armed Bravery, Combat Reflexes
LV10. Spellcut
LV11. Weapon Training > Advanced Weapon Training > Fighter's Reflexes
LV12. Smash from the Air, +1 STR
LV13. Greater Weapon Focus (Heavy Pick), Weapon Training > Advanced Weapon Training > Focus Weapon (Heavy Pick)