Ford 3.6L Engine making a tinny rattling sound?

I recently tore apart the 3.6L V6 in my '95 Mercury Cougar. It had spun a bearing. I replaced the bearings, the blown head gaskets, and the lifters. I got the engine back together last night. After I started the car I there was a loud rattling coming from the engine. It is not the same sound the spun bearings were making before the repair. At first I hoped it was the lifters getting pumped up; it did make a bit more noise at first, but the lifters settled and the noise continued. It is louder when the car idles. If I press the throttle the sound quiets. It sounds as if something might not have been tightened, but I'm not sure. I checked and all of the transmission bolts are on tight. Any suggestions on what to look for would be appreciated.
I did not have it machined. We measured things and I replaced the bad bearing with an undersized one that fit. I know this is not the ideal solution, but it was a budget issue as much as anything else. I fear we may have to tear the engine apart again.
I didn't "ruin a perfectly good engine." For one, it has 155K miles on it. I'll be honest with you, I'm just trying to get the car in good enough running condition to sell it as I don't drive it anymore. I never said it was a rebuild, as I realize it wasn't a complete rebuild. If I planned on keeping it I would have gone that far.
To the most recent answer, yes, I oiled the bearings before installing them.
 
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