What kind of heads do I have?

Yes that's them they have a compression height of 1.810 that will really help with compression you could also mill the heads and deck the block and bring it up more. But with milling you have watch your push rod length and rocker geometry.
You should take this advice and use it on everything, stock or modified, cut or uncut.
You are correct I misread my book. Depending on the year....... My "How to hot rod small block Mopar engines" book shows the 71-76 360 head to be between 65-73 CCs, then the 77-89 to be 66 to 72.5 and 90-92 to be 68 to 74.5 CCs.
The book shows the low cc amounts as a min chamber size.

Those heads (360) would work well with some pop up pistons to compensate for the CCs?? Since he's building the engine anyway it won't cost much more to get high compression pistons??

treblig
Custom slugs? They can be expensive. Or VERY expensive. A domed high compression 318 slug is hard to find at best.
Killing the heads for a better ratio is a catch 22 as you know because of the fitment issues created.
Between the flat top KB’s, HyperU’s or forged, decked block & milled heads, you can do pretty good. But it is a PIA.

Being a little light on the ratio isn’t a bad thing. Being light a 1/2 point off the recommendation of the cams suggested ratio is OK. 1 point down is approaching crummy. The closer you are to the recommended ratio for the cam is for efficiency. I would not want to run a cam like, oh let’s say, [email protected] in a 8.0-1 engine. It would be way happier in a 10-1.

Just remember IQ52’s threads on compression and cylinder head flow. Flow will trump compression every time. LMAO, and people trashed the MoPar advice of 360 heads on a 318 even though Jim backed up the MP advice with his dyno tests.