You have to be careful when talking about 'speed' when you make time a dimension in your geometry. Traditionally, speed is a measure of how much of your space-time curve is in along the time axis.
For any space-time path, you can consider the coordinate system as an observer traveling that path would see it, in which that observer would see itself traveling through time at a rate of one second per second. Geometrically, if you were to draw where on the path the observer's clock ticks, the distance between ticks as measured along that path is constant regardless of the path.
The speed of light limit says something different. It limits what paths a physical observer can take.
Condsider a 1+1 dimensional universe (or our 3+1 universe with a test particle moving along a single spatial dimension).
Pick a non accelerating observer to construct the 'stationary' coordinate system. Plot spatial coordinates along the horizontal axis, and the time coordinate as the vertical axis. Pick units such that the speed of light is 1.
A particle moving at a constant velocity will follow a straight line. If the line is vertical the particle is stationary. If the line is at an angle, the speed of the particle is the inverse of the slope of the line. The speed of light limitation says that this line cannot be shallower than 45 degrees.
In more analytic terms, the distance metric for our 2 dimensional spacetime is given by ds^2 = dt^2 - dx^2. The speed of light limitation says that ds^2 cannot be negative for any path a particle actually takes.
In other words all particles must must have at least half of their travel be along the time dimension.