I think ONE portable air con unit, 15000 BTU £450, has two 125/150mm ducts and might use one as intake & one as exhaust. Big & heavy & noisy tho from the specs.

Split air con, even DIY, comes under new F-Gas regs.

BR specifically (as I recall) prohibit chimney's from being used as ducting, that may be re grease buildup, moisture buildup, or affecting neighbouring chimney gas fire operation.

For the fan method, you need two 6" fans mounting on plywood to an upstairs opener, with 1-2 300x300mm flyscreen mesh grilles mounting on plywood to a downstairs lower casement (or old back door). That will make a difference, but it really needs a large panel fan at reduced speed (get the size without the noise). Two 12" fan for south facing is better, but that is as costly as air-con - although proper air-con needs to be about 24,0000 BTU to really contain temps downstairs in a house and even then you need solar blinds and so on.

Never understood why portable HVAC did not come with a proper two duct option, yes it needs two windows or two vents but at least the OPTION for making the thing work /as well as air-con is capable/ instead of "lame" is there..