From a foreigner perspective it seems to me you clear customs at EDI

OK, this is from Nothing To Declare, if UK Border Force wants to speak to you, they flag you up for interception and questioning when you exit. I imagine if your bags are being through checked to EDI they will know this and intercept you at EDI - no point intercepting you at LHR without your bags.

This is reinforced by my three visits to LHR in Feb (I did not avail myself of the transit gate for any of my visits, I rather land and get some landside things done like mailing or simply using First Wing even on a T5-T5 connection) I don't see a Border Force officer in immigration for two of the my three entries into the UK.

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As an aside, I think this is similar to US Preclearance, which was also part of my trips.
I don't walk through CBP with my checked bags before check in. During preclearance immigration, at one time the Preclearance officer confirmed with me I had one bag checked in.

I suppose if they want to question me about my bags, they too intercept me at my US domestic arrival point?
They have that right to intercept me before I walk through the domestic airport exit gate (I can't remember where I read this). Most likely when I attempt to pick up my bags. I better strike out the analogy to US Preclearance - I've been told they try to intercept the passenger before the passenger leaves the Preclearance part of the overseas airport - either at a security checkpoint or at the gate.