Ahh.. That's the Model C reproducer, used to play 2 minute wax cylinders.
Here's a picture of a couple of mine.
The first one is the same as yours, which has Model C printed on the "fish tail weight", and the two holes drilled in it. These holes later disappeared (I think during 1907?), and were originally meant to enable more small weights to be added, but I've never seen one with the extra weights.
The second one, without the F/T weight, is a recorder & not a reproducer. You could buy blank wax cylinders, and make your own recordings at home with one of these.
The third is a Model H reproducer. These came out in 1908 when Edison started making 4 minute wax cylinders. The grooves were half as wide as those on a 2 min cylinder, and required a stylus/needle half the size of the Model C's. Convertion kits were made available to convert 2 minute machines, to play both 2 & 4 minute records by altering the gearing, so the reproducer could move across the record at half the speed but still have the cylinder revolve at 160rpm. The Model H reproducer was included in this kit.

So, your machine is a Model A, with a model C reproducer.
It's definately a model A, because it has the speed control knob at the front left hand corner. This knob was no longer used on the Model B range, because the speed control was then only accessible from the underside of the bed plate with the motor (thats what the black painted part that the upper works & motor attach to is called)
I must admit I'm a
little confused about the colour of the cabinet. The very last of the model A's did get finished in the "antique oak" colour which the Model B's had, which yours appears to be in the first photo.
I noticed though, that in a couple photo's of the upper works you posted, the wooden bedplate frame looks like it has a few spots where the "green oak" colour is showing through.
Now, whether those areas are just where the finish has worn off, or if the machine has been refinished over the top of the Green oak colour- either by Edison or somebody at a later time, it's hard to tell from a photo. It would be much easier to determine by actually looking at the machine in person. Then again, it could just be years of furniture wax & dirt.
Something I've noticed, is that your reproducer is in upside down. The fish tail weight should be at the top, rather than at the bottom as in your pictures. If you loosen off the little screw sticking out from the black ring the reproducer sits in (at the 1 o'clock position), you can lift it out carefully, and turn it around. If you look at the round "body" of the reproducer, just above the F/T weight, you'll see a little slot cut into the edge. There's a little pin in the black ring "reproducer carriage" that fits into this slot. Once the reproducer is sitting flat in this ring with the pin in the slot, you can then tighten up the little screw to hold the reproducer securely. This is so the stylus lines up with the groove correctly, and so it can support the weight of the small witches hat horn.
In the photo's, the finish looks quite good, and if it is the original finish, I would advise against having the cabinet restored. Most serious collectors don't want machines that have been refinished. They much prefer machines to have the original finish, even if it's not perfect. A few spots of wear or light scratches etc, are perfectly acceptable for an item that's over 100 yrs old, and was probably the families main scorce of entertainment for a generation or two.
Like I said earlier, I think if you give it a good clean & wax, you will probably be surprised at how good it looks, once 100 yrs of dirt, dust, furniture polish etc etc is removed. Although you might never want to sell your family heirloom, a machine with a good original finish will always hold it's value better than one that's been refinished too..
Is there any chance of posting a picture of the console phonograph you spoke of?
Is it a cylinder or disc phonograph?