You could consider using an Ethernet Extender. These typically use VDSL2. Note you will take a big performance hit compared to standard Ethernet. https://www.snappernet.co.nz/products/category/13/ethernet-extenders Personally I would compare the cost of running fibre plus a PoE injector versus an MS120-8P. The MS120-8P will regenerate the signal, will support PoE, and will provide a management view of what is happening (plus allow cable testing in both directions). My personal guess is using an ME120-8P in the middle will work out cheaper.
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