This appears to make sense in conventional physics.
Problem is that this whole problem lies comfortably within the world of plank's constant and quantum mechanics, with some help from special relativity and general relativity.
There are a lot of problems with this idea.
The first is that to slow down the photon it needs to be shot into a very dense object.
The essential problem is that this won't be a simple machine with an off on switch.
Photons behave like waves when they are interacting with other photons and like particles when they interact with matter (and I stress the word LIKE in both cases).
They are chargeless and have no mass. That means that your machine cannot work on the basis of electromagnetism to slow down photons since a photon has no charge. And you can't use some sort of 'light field' because light will behave like a wave when it hits the field and won't be affected at all because there's no way to create a field where you can perfectly shift the phase and compensate for the different frequencies of light striking it fast enough to shield what's inside.
Anyways, theres one even bigger problem.
If at time=0 seconds there is light departing from the object to be shielded and at that instant the "machine" is turned on then you have the old image of the object still travelling to the observer at 3*10^8 meters per second (the speed of light).
But directly behind those lightwaves are now the ones that have been slowed down to around 26 meters per second.
At time=0 those two sets of photons are at the same point.
But in a mere second the first set has travelled several thousand times faster then the ones that have been slowed down.
So the observer sees the original image, but once those photons pass by him he no longer sees the original photons, and he cannot see the ones that have been slowed down because they are still a long ways off.
So all that he sees is a black bubble where the machine is, at short distances it means less then a second, at great distances it can mean several seconds.
In essence, this machine essentially makes a black bubble which is completely obvious to any observer.
What's even weirder is that once the machine is turned off, if the observer is far enough away, he will see the new "not slowed down" photons before he sees the ones that have been slowed down.