"Compressive strength is identical to tensile strength, as long as buckling isn't an issue. For example, a short thick block of metal will stretch or compress by the same amount if the same load is applied in tension or compression. Your calculation for compressive loading is only valid for short thick blocks of metal."

Compression and tensile are not identical. For example concrete has significantly higher compressive strength than it's tensile strength. Cast iron has fairly good compressive strength and not a very good tensional strength. Though generally speaking there seems to be a correlation between the compressive strength and tensile: Diamonds have extremely high compressive and tensional strenght. An anvil [or good hammer] would be made of steel which has high compressional strength, but I would imagine it would also have a high tensional strength. And piano wire which has very high tensional strength would also have a fairly high compressive strength. Though it seems to me that steel generally can be made to have a significantly higher tensional strength than compressive- but this may be mostly due to there simply be more demand for the tensional properties of steel, whereas with concrete there is much demand for it's use as compressive material.
And compressive loading is not limited to short blocks of metal.

"There is a ratio of length-to-diameter when buckling becomes a problem. Getting into the math isn't the point, just think about the first paragraph above. Your lunar tower will require guy wires to support it."

First, I wasn't presenting it as a "done deal"- the first thing this 150 mile (or taller) tower would do is drive down through the lunar surface- if the lunar surface had any where near it's compressive strength, I would use lunar rock instead of steel. This tower on the lunar surface would be like you trying to stand on water:). But assuming it's base was properly supported, this 48" diameter cone should not buckle, unless there were additional forces acting against it or an inconsistency in the material strength. One force which would act against it is thermal differences from sunlight. For purposes of a lunar tower, guy wires aren't going to help, they designed to counteract forces such as wind.
Unless you mean a cabal from space elevator is the "guy line" I don't think it can be argued that a lunar tower would require guy lines.