My lovely new bike.

[Xrayted]

Welcome!
Keep at it. You're doing fine.
A few things: from pic of your bike (nice, btw) it looks as though your brifters are really high, almost on top of the handlebars. (or are the bars tilted back too much?) Does this position feel okay to you? Why I'm asking is... if you are in the drops, I can't imagine that you would be able to touch them at all. Also, when they are that high up even when you are on top, it pulls them away from your fingers and shoots them straight out. The only part close enough for you is at the origin of the brake so you are working too hard to pull them or get into another gear. (think physics... levers, teeter totters... hard to push/pull close to the fulcrum) If you need them over the top like that, you may have to get a shorter stem to bring the reach closer, not move the shifters towards you.
Also, it's true that a bike mech may get it shifting great on the stand but when you get it on the road under "load" conditions, it doesn't go well. I had that problem and got tired of taking it back to them so I looked it up on Sheldon Brown's website and set my own derailleur. It took me a few hours of messing around but it works great now. I don't have to push further or hold it to get it to shift correctly to a bigger ring. I have 105's on mine too and they shift the same up or down now. LBS setting... kept dropping the chain, not getting the whole way into gear without pushing a 2nd time, etc.

You may want to check the width of your handlebars and make sure they are right for you. Your arms should be lined up with your shoulders, not out to the side. You can easily get shims put in. Any LBS should be able to install them. They are easily ordered and I would be surprised if they didn't keep a pair in stock back in the shop area.

Knot is right, you did good getting a frame that fits. The rest gets adjusted along the way but there's no adjusting the frame. (those pesky welds ya know)

Take care and be safe.