Your proposed design, shown in the PDF "Preliminary Design", should work great as a retrofit to the original weak-post guardrail to culvert attachment system. By extending the length of the socket with the height of the headwall, you will limit/reduce the lateral load transferred into the headwall by the top anchor rod (longer moment arm between tension at top of socket and compression at bottom of socket equals lower loads with same bending strength in post). Since it sounds like you are retrofitting the headwall to an existing box culvert, limiting the loads imparted to the headwall and the connection to the culvert is probably the best course of action.
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