I would get a copper head gasket from either Moss or BPNW. Sure I bet the wire idea would work; it is basically smashing more copper in the liner area. I would was the copper wire trick in a pinch.
When I check the liner height, I first get my eye down on the block and have a look at the top of the sleeves. I can usually see that little bit. Then I measure with the feeler gauge to see imperfection. I have never had block the was under .003 so not sure what to do. On engines I have built some spots are either hard to see or difficult to see and were .003 to .005 kinda even with new liners. It comes down to, do you think there is enough to seal the head on top of the sleeves.
Every time I build an engine I worry, are the fluid going to mix.
It sounds like you have a certain spot that needs addressing. If I figured the chances of leaking were kinda good, I would probably take the pieces to a machine shop to have another set of eyes on it, or take some real good pictures and ask the guys here, or do both.
Steve