top dressing, MO Bacter and the moss farm...

Hi everyone, I have a phenomenal amount of moss on my lawn this winter, really dispiriting as I do try to do all the right things, aerate, top dress, scarify and whatever else.  

However I have found an RHS recommended product called MO Bacter which kills moss without the need to scarify the dead moss out - it is apparently digested in situ by enzymes which sounds just dandy to me - and as there is nothing chemical or harmful in the mix you can sow seed pretty much at the same time, thus shortening the time till the lawn starts to look good again.  That anyway is the theory, and I plan on doing this in about March when the weather has warmed up.

But I want to once again put quite alot of top dressing on the lawn now to go some way to improving the drainage, and to build up some edges where they slope down towards the beds and get scalped by the mower.  However.  Can I put the top dressing on now and what happens to the moss?  I know grass will grow through top dressing layer eventually but I imagine in large areas of the lawn the top dressing will just 'sit'  on the moss.  Is this OK, a good idea, or a bad idea?  Or do you think I should just tackle the unevenness around the edges now and try to deal with the large mossy areas in the autumn?  I have been doing this for a while, ie building up the lawn in the autumn, but it just doesn't seem to get any better.  It is shady-ish at that end of the lawn, but not THAT bad.  It's not deep deep shade!  Any ideas v much appreciated, hanks.