Stop using anything soapy on your skin, whether soap or a foaming cleanser. Use something creamy, a balm or milk, apply to dry/damp skin, remove with warm flannel. You're drying out the oily bits which makes them oilier. More oil = open pores. I love Clinique Take the Day off Balm, Emma Hardin Moringa Balm, or an oil cleanser - there's a Vitamin C one in Boots, can't remember the brand.
Same for moisturising, don't skimp, if you pamper and hydrate your skin, it calms down. A good serum, plus a light oil free moisturiser. Maybe experiment with Hydraluron / hydraluronic acid (hydrating) later on.
Tons of water, good fats, EPO supplements.
I have been in exactly the same boat for years (I'm 36, so not peri-menopausal yet, but same issues), and my skin is so much better for this regime. Not perfect, but so much better.