Imagine a bunch of cars on a road. They all travel at the same speed, but all the red cars have a special lane to themselves.
The cars come to a tunnel. Inside the tunnel, red cars have to travel at half the usual speed, but the other cars can carry on as normal.
Once they get to the exit, the red cars can speed up again.
What happens is that you get a delay on a *particular* red car, but overall the *rate* of red cars after the tunnel is the same as all the other cars.
This effect applies more for transparent or near-transparent material. Most of the Sun is pretty opaque, so it's not really best to think of it as the "same" photon bouncing around until it escapes. It's better to think of it as photons being absorbed and new photons being emitted. This is important, because the photons we see give us a picture of the surface of the Sun. The combination of wavelengths of photons that we get is right for photons emitted at ~6000 K, the surface temperature of the Sun. The core of the Sun is more like ~1,000,000 K, but these photons do not reach us directly.
What we get is photons emitted very close to the surface, which then only pass through very thin plasma before reaching our eyes.
Faster speed does not increase the number of collisions in a random walk; it only decreases the time needed to escape the sun because the collisions happen faster. The main thing that matters is the chance of scattering (which affects the number of collisions). According to [this lecture](http://farside.ph.utexas.edu/teaching/em/lectures/node96.html
), the scattering is not dependent on wavelength.