Visualizing 3×3 spectrahedra

If the desire is to not have a surface appear when the region hits the boundary of the plot range, you could use something like:

Show[RegionPlot3D[Evaluate[cons], {x, -3, 3}, {y, -3, 3}, {z, -3, 3}, 
  PlotRangePadding -> None, Mesh -> 5, PlotStyle -> Opacity[.7], 
  PlotPoints -> 10], PlotRange -> 2.9]

to truncate the plot range to an area inside the boundary.

For plotting 3D surfaces, there's ContourPlot3D. Here's an example from the documentation:

ContourPlot3D[x^3 + y^2 - z^2 == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]

However, I can't modify your code because no matter what I change it breaks, so this is all I can give you here. Could you clean it up a bit and document what it's doing so we can actually play around with it?