Hmmm. My experience has been very different. After winning games on settler (for fun), noble, and prince, I'm not sure I've ever been attacked - and if so, it must have only been once and not that serious. (This is not counting the one time an enemy I'd previously had a war with decided to take a revenge shot at me.)
I have won all these games space race or diplomatically. I cannot say for sure, but I THINK the reason you guys are being attacked might be that you're 7th in power.
I mean, who would you pick to attack in this example: You just got through the early game and had to expand west and north instead of south where you first wanted to because another civ got there first. Then the resources start showing up and you see both iron and oil, which you lack, in the radius of one or two cities to the south, and oil and coal near 1-2 cities to the west. Who do you attack? I hit the guy with the weaker army, in all likelihood (though I admit I'd think about who was likely to vote for me if I'm going for a diplomatic win). I'm presuming the AI is doing the same we are - coveting the goodies!
I'm sure you are careful builder players, as you say. So just watch your "Power" graph and ranking and don't drop below 4 (I prefer 3 out of 7) - keep your military more modern with either upgraded or newly built units. One large stack in a fairly central location in a medium sized empire should be able to reach most of your cities in 2 turns or so via roads, wouldn't you say?
And if the #1 or #2 "Power Graph" nation demands something of you when your army is in the #7 spot? GIVE IT TO THEM.
That's my suggestion. (I got attacked a lot in Civ3 early on, and I noticed that a stronger military seemed to do a lot to make the AI think twice.)