Hugh,
P.D.4. is an unknown mark, possibly Polizei Direktion. I have P.D.18. and P.D.471. in my database. Here's a discussion about the latter:
http://www.gunboards.com/luger/topic.asp?TOPIC_ID=1844
I believe you're correct about S.G.I.290 being from the Gumbinnen District. Gumbinnen was the easternmost district in Weimar Prussia and was deep within the Soviet zone after WWII. Yours is the only example of a Schupo mark from there that I know of. I only have one Landj�¤gerei mark from that district.
Could you post photos of both marks? I would sure like to see them.