The motor is quite small, but it should make for a nice learning experience. The number of slots (16) restricts your windings to a single phase configuration, but i would not worry about it too much as it will be a small machine.

I would not bother trying to rewind it.
I would turn the rotor down to hold those magnets 2 deep, and a bit more.  Each pair would be "one magnet".
Then I would mount 8 magnets One Deep: 2 N, space, 2 S, space, 2 N, space 2 S, space.
Then after the epoxy is cured, add the second layer. (easier that way)
Total magnet count is 16.

The first layer being close to each other will not want to lay flat, so it takes a little extra space to make up for any tilt they do.

One pair of wires will make some power.  Not much.
The others will probably not make anything worth trying to get. But if they do, the common connections (in the paper under the zip ties) will need to be separated.  I would separate them for testing anyway.

I expect it will end up high voltage and low current.  Low cut-in RPM (relative to a suitable blade size).  May be better suited to a low TSR 5 blade prop.

It is a big job to change the windings in something that small.  There is not enough room to work.

How about making a single large coil and wave-winding it all at once. Is that doable?