I looked at my last 11 scores. One the first hole I had 6 pars and 5 bogies.
• When I parred the first hole I averaged 79.3.
• When I bogied the first hole I averaged 79.2.
When I reexamined the original question, "Does a really good or bad score on the 1st hole tend to have an effect on how you score the next 17?", I rationalized that pars and bogies are not really good or really bad. To be really good it has to be a birdie, to be really bad a double bogie or worse. So, I looked at the rest of my scores for 2014.
All of my opening holes this year were all pars and bogies, so I looked at 2013. In 2013 I opened a round three times with a double bogie and averaged 80.3. I had to go all the way back to November of 2012 before I started with a birdie, and that day I shot 82.
So, in my case, an opening hole score has little affect on my score for the round.
Little effect on your 18 hole score, but a small effect on the score you make the next 17 holes.
Assuming that you always opened with a par 4, then over your last 11 rounds, for the last 17 holes you averaged:
75.3 when parring the first hole
74.2 when bogeying the first hole.
For the 3 rounds you made double, you averaged 74.3 the last 17
For the round you started with a birdie, you took 79 the last 17
Your detailed record keeping seems to indicate you play the last 17 slightly BETTER when you get off to a bad start (but it is not a very statically significant sample size given just a 11 rounds and a cherry picking of the rest).