Engine Miss

I have my Son's 2000 Tacoma w/3.4 V6 I am working on.
It has a miss and sometimes a backfire thru the exhaust ONLY after it has come up to operating temperature. When the engine is cold it seems to run fine.
When cold the engine idles perfect and drives fine until it warms up.
When warm, it misses at idle, also when building speed, but seems to smooth out at about 55 mph. If you try to build speed above a cruise speed the miss returns.
The CEL stays on steady until the engine starts to miss then the CEL flashes.
We have run the codes and came up with PO300, PO301, PO303, & PO306.
We know what the codes mean and have changed the plugs and checked the compression (it was good) since reading the codes but no good results.
I am hoping someone might give me info or opinion on this before I sink a ton of money into it unnecessarily.
Thanks in advance for any help!

 

Arkansas,

Do you know if and when the timing belt and idler were replaced? It is typically recommended to do this around 90,000-100,000 miles.

 

According to sticker on timing cover the timing belt and idler were replaced by Toyota dealership 82,000 miles ago.

 

Any word on this?

If you did a compression test, a cylinder leak down test is another good idea. If you have the capability.