Now, I have some philosophical questions: If I had been solo mining, would I have still mined these two blocks?
If you had managed to solve the blocks while solo mining then you would have mined them but you had no way of knowing you would get so lucky.
Also with 13 GH/s you will get a very high variance, I think it's not worth it with such a slow speed nowadays. With the increasing difficulty you might as well never solve a block.
Did choosing to mine in a pool cost me $5K?
One could say so but the chance that you will again mine 2 blocks in the same span of time with current difficulty with current hardware is very low (you can say you got very lucky (or unlucky depending on the way you look at it)).
Could someone who understands the nature of luck please help me with these confounding questions?
You just got very lucky here but in the long term the profits will even out (the greater the time span the higher the probability that you will mine the amount of BTC that corresponds to your hashing speed and mining difficulty).
Am I clearly a lucky miner and should begin solo mining immediately? Should I buy a lottery ticket? Or did I use up my luck and need to stay in pools forever? Should I look both ways twice before crossing streets?
No for all of these questions, solving one block doesn't affect the probability of solving another block because these are independent events.