Either way will require equal pressures so need to get a tank cold feed to the shower also I don't think the pressures will be good enough might have to go down the pump road
I've fitted tank cold feed in 22mm and will pipe both hot and cold in 22mm to within 1m of valve. Only got 1m head which spec says is min gravity pressure - if customer is not happy with flow rate will have to negotiate on supply and fit pump.