you can get Panasonic TSUPs at 25v/ 10000uF that are 20mm high and 35mm diameter and 35v/ 10000uF 25mm high and 35mm diameter. Problem is, I can't find that physical size on Farnel or RS!

I'll see if I can source them! but i'm fairly sure that they will fit. Otherwise you could try something physically larger on its side??? Not ideal but would work if space permits