340 .040 Bore Okay?

I recently purchased a 340 engine that was “completely rebuilt” that the original engine builder said would be a great engine. Engine had sat for a few years / never installed. Thought I would do some checking before putting it into my dart. Fortunately i did. The list of issues I found are too many to list. Tearing the engine completely down. Variations exist with the bore size in each cylinder. Hard to believe! The largest .030 with rust. I know plan on having it bored to .040. Is this too much for a 1971 340 block? Will I run into overheating problems? Thanks in advance for any information.
I just got off the phone with the machine shop owner who is working on my +.040" 70 340 block. He was roughing in the bores and found a sleeve in the #4 cylinder already. He is going to sonic check the block as he is getting ready to replace that sleeve because he did not like how it was installed 24-25 years ago by another shop. After the sonic check, he is planning on going to +.050" on the bores and purchasing custom pistons.
Sonic check it!