I've never experienced a leaking slurrystore, but I would think that the first thing you need to do is to get the level of manure down below the point of leaking, to help take pressure off that leak. 

How much snow cover do you have?  Is spreading manure this time of year an option?  or is there too much snow cover?  

How far up the side of the slurrystore is the leak occurring?

How tall is the slurrystore?  and how full is the manure?

What did your dealer say about the leak?  I would think a dealer would be in the best position to know how to fix the problem...... once it is emptied. 

Depending on whether you have the leak stopped, you may decide not to spread the manure "today", but may want to keep your eye on it, until you see a "window" where you can get it spread.

BTW, if you normally spread the manure yourself, this might be a good time to have a commercial hauler lined up to spread it; when a window presents itself to spread manure, that you can get it spread quickly.  I don't know if this is pertinent or helpful, but I thought I would toss the idea out there.