You might want to include your recipe for the buttercream. That could help people figure out one of the reasons for your cake layers sliding around.
My thoughts from looking at your luscious cake photo are:
3 layers is a pretty tall cake! 2 layers would be more likely to stay stable. If you want 3, you could make them thinner, or even cut one of them in half. As long as you don't have a sliced edge at the very top, it doesn't matter that frosting will kick up crumbs from the sliced edges.
Layers don't look quite level (i.e. flat). You mentioned leveling the top layer. Maybe more important to level the bottom layers, if you don't want the upper stories sliding around.
Is buttercream a little too liquid and slippery? Knowing your recipe might help people determine this.
Possibly a little tooo much buttercream in between layers. I don't mean too much to be delectable; I mean too much for mechanical stability. It's hard to tell how much is in between the layers, but it does look like a pretty thick coating on the outside, so I'm guessing you were also generous in-between.
All that said, this cake looks terrific, and very rich!
You can make the base wider with white chocolate. No glue, and you can do it in advance so you don't need to have any electricity at the site.
Put a parchment paper round into an appropriately sized cake pan or a plate or shallow bowl. Stand the cake topper in the middle of the parchment paper. Carefully pour or pipe melted chocolate around the edge of the base and build it up, coating the base and widening it. Allow the chocolate to cool, carefully peel away the parchment paper.
If the weather is likely to be warm, you may want to make the additional chocolate layer thicker so that it will not melt quickly and release the topper.
You could also widen the base with some other material (cardboard covered with foil, for example -- make a large cardboard disc, cut a hole in the middle for the stem of the topper, cut a slit on one side of the hole the size of the base, slide the base through and center it) and cover that with chocolate or frosting, but I think plain white chocolate would work well and it sounds like the bride wants to keep everything touching the cake edible (except the topper itself, of course).
Best Answer
You might want to include your recipe for the buttercream. That could help people figure out one of the reasons for your cake layers sliding around.
My thoughts from looking at your luscious cake photo are:
3 layers is a pretty tall cake! 2 layers would be more likely to stay stable. If you want 3, you could make them thinner, or even cut one of them in half. As long as you don't have a sliced edge at the very top, it doesn't matter that frosting will kick up crumbs from the sliced edges.
Layers don't look quite level (i.e. flat). You mentioned leveling the top layer. Maybe more important to level the bottom layers, if you don't want the upper stories sliding around.
Is buttercream a little too liquid and slippery? Knowing your recipe might help people determine this.
Possibly a little tooo much buttercream in between layers. I don't mean too much to be delectable; I mean too much for mechanical stability. It's hard to tell how much is in between the layers, but it does look like a pretty thick coating on the outside, so I'm guessing you were also generous in-between.
All that said, this cake looks terrific, and very rich!