They look like microwave magnets to me.
The pics don't show how big the coils are compared to the magnets, but they seem a little small. The center (hole) of the coil should be as big as the outside of the magnets.
Maybe you could change the magnets to 2" neos? You could use what you have, and it would not cost TOO much. (it never costs much if it is someone elses money )
Maybe 3/8" of each side of each magnet could be cut off, then double them up?
Could each existing coil be rewired, one of the starts to one of the ends, to give 80 turns of #17?
I hate starting over.
Thinking out loud.
G-