I came to the many of the same conclusions. After I left the JW's in 1992 I began visiting several "conventional" churches and I was especially interested in the subject of prayer. During my JW tenure, I did not see any evidence of God responding to such petitions.
I found the same in the other churches. Many of the prayers were generic and vague asking God for strength in helping to cope with an issue, or help in finding a job or heal an ailment. What I found was that it was a crap-shoot. The folks who prayed would wait a bit and then fit the conclusion to what they prayed for. If God acted positively then the answer was yes, if not then it was no.
I have heard many, many anecdotal stories regarding how God answered their requests, but I never saw anything divine in them. The vast majority could be explained as just random and flip of a coin, others had answers that could be explained by science or the fact that the person who prayed actually did something to ensure that something positive happened.
What was amusing is these results are found in every group or religion that prays. I could not find one instance where any belief system had a lock on the act of prayer.
I always chuckle when I hear the ad for "Christian Mingle.com" where the announcer says instead of waiting on God, he is waiting for you to act. In other words, you need to put forth effort to get a result. Sounds like the natural world to me.
Donny