Originally Posted by FBinNY

There are two conditions that must be met.

The first relates to the local stresses on then post and the tube when the post is loaded sideways. Think about a fencepost in a too shallow hole. If not deep enough, the post or hole distort and it tears out. The rule of thumb for this is about 1-1/2 diameters minimum (note the height of threadless stems which are subject to the same rule). But that's only half the story.

On frames where the seat tube extends above the top tube, as do most frames these frames. The post cannot depend on the extension for support, so that 1-1/2 diameters rule applied from the height of the cross braces, and as a rule, you want the post to extend well below the bottom of the intersecting tube, and this is usually the defining issue for adequate insertion.

So, 1/2-1" below the bottom of the cross brace, or 1-1/2 diameters whichever is greater, and you should be fine. (which by your numbers you are).

Lastly, one more condition which applies to heavier riders and on bumpy roads where there'll be plenty of back flex over time. The post must be stiffer than the seat tube, otherwise it won't properly support the tube and the bending stress will lead to cracks at the base of the seat tube extension. This third rule is often overlooked leading to decent numbers of "mystery" frame failures even when the post went deep enough.