Affordable gear to get shallow depth of field at standard focal lengths?

I’m just looking for some recommendations on affordable gear to get shallow depth of field from a standard focal length of 35-50mm equivalent.

I currently have a Sony RX100M3 and a Sony RX10. The RX100M3 is great as a pocket camera, but the short lens makes it not possible to get significant background blur. The RX10 can do this due to its longer lens, but of course that’s only at longer focal lengths with a much tighter field of view.

I’m sort of looking to fill the gap and be able to get shallow depth of field from standard focal lengths, and the only way to do this would be combining a larger sensor with a fast lens.

I realise I probably need to look at an interchangeable lens camera for this. Cameras like the Sony RX1 and even the Fuji X100T are outside my budget. The Canon G1X Mk II has an almost APS-C sized sensor and fairly fast lens, but it’s probably not going to be a match for an ILC with fast prime.

Canon and Nikon have cheap 50mm lenses to go with their APS-C DSLR’s, but of course the full-frame equivalent focal length of these is a bit tight at 75mm or thereabouts.

Micro four thirds is an option. A cheap body with the 20mm (40mm equivalent) f/1.7 might give me what I want – although the sensor is a little smaller than APS-C.

Now my thoughts have turned to the Canon EOS-M series and the 22mm (35mm equivalent) f/2.0. Not that the system has much interest for me, but that lens is available very cheap on eBay and I could pair it with previous generation M2 body for quite an affordable option.

I’d be interested in any advice – thanks in advance!