flumpery

For heat management - green roofing is actually a reasonable solution. It retains more water and absorbs/retains more heat. GRO (https://www.greenrooforganisation.org/) will have more info on this. GRP is a good material for roofing as it's durable Issue with fleece backed epdm is that it is vulnerable to being punctured. Some flat roof systems come with guarantees for 20 years so that may be an option if you want that security. BBA certificates are a good way of determining longevity and quality too

Hey David Jumping on this a little late; but just in case anyone else sees this: for over timber rafters or counter battens, installation guidelines for most breathable membranes require there to be a drape in order for them to function properly https://www.roofgiant.com/breather-membrane-guide/ https://www.roofingsuperstore.co.uk/help-and-advice/project-guides/pitched-roofing/how-to-install-breathable-roof-membrane/ However they can be installed fully supported with sarking board or rigid insulation as is the norm for Scotland roofs (usually put in new build or refurbishment in more extreme weather prone areas) Also of relevance - for sarking boards if you have a tiled roof the "use of counter battens and tiling battens over the breathable membrane allow for water drainage and attachment of the tiles" [https://www.kingspan.com/gb/en/knowledge-articles/what-are-sarking-boards/]