Yes mould cleaner will remove the Easylease. You shouldn't need to use mould cleaner anyway, there's no issue with what is on your mould. The issue is that you are trying to apply a liquid to a surface with very little energy, so the liquid adheres to itself easier than it adheres to the surface. This causes the droplets of liquid to form the shape that requires the least amount of surface area, a sphere or 'bead'.
There's no easy solution for this as it's a simple physics issue. The best solution is to spray the gelcoat. If you have an area where you can spray, borrow or buy a compressor and a cheap HVLP gun (preferably with a 2.0-2.5mm tip). Then the technique that Alex described works perfectly and is the best way of applying an in mould coating.