As a PPL I am ashamed to say I have never contacted a military airfield.
Full marks for asking but I'm disappointed that wherever you did your PPL course that a MATZ penetration was not included as part of the training unless maybe the location was a long way from a MATZ?
Whether you're aiming to turn overhead isn't that relevant - just ask for a MATZ penetration and give details of your intended routing. Be advised that military airfields are QFE oriented so you'll usually be asked to adjust to fly at a height on their QFE. If the airfield is a significant elevation above sea level this might put you into cloud so something to take into account if you're aiming to maintain VFR.
If you don't get a reply to 2/3 calls then you can assume the MATZ is not active so you can penetrate but as has been said above remain clear of the ATZ since although the main military activity may be closed some airfields have local military flying/gliding clubs which may be active.