This hand was from a 8-game MTT but the format isn't relevant. Hero has tight winning image. Villain is good pro slightly TAG/LAG. I am interested to see if this line I took is good or bad?

I open 8773Q from CO and Villain 3bets BTN, blinds fold, I call and draw 2 to 873. 2:2

I catch A7. I have now seen three 7's. My plan was to check and if he checks to draw 2. If he bets I was going to snow however I didnt want to go 2 to pat because most of my 2 to pat range is going to be rougher, containing a lot of rough 8s that will want to check river oop. But I need to bet river to snow, so I opted to draw 1, and snow next street repping a smoother draw that could make hands worth value betting river. So I x/c and drew 1 to A783. Villain drew 1. 

I check, he bets, I c/r planing to pat and bet river. Thoughts on the line to this point?

Villain 3bets, and I cap, villain calls. I felt like he was often trying to get me to break and I thought most 86's he would flat my c/r so he is mostly repping 7's which I block. I pat. He draws 1. River I bet.

Is this play better than just drawing 2 again to 873? Is it better than some other option involving snowing?

Pros: 

My image is tight and value oriented. I don't think he thinks I'm capable of snowing or at least often in a spot like this. 

I think he is only going to SD with an 8 or better. I should get a fold about 80% given he will go to 2-to-pat for an 8 or better 3% of the time on 2nd draw and on last draw he will go 1-to-pat 8 or better ~17%.

Cons:

I sacrifice my ~25% equity with 873 vs his range of pat and 1-card draws when he bets and keep the A.

If he makes an 86 he is probably calling down; in those spots I put in multiple bets dead.