Because I am an amateurish cue maker that likes to practice on cheap cues I can pick up for cheap.
Fair enough.
You might want to consider what you expect out of the project, tho. If you just want to practice finishing, go get some cheap hardwood, turn it round and practice finishing. Cherry and walnut are relatively inexpensive, but both will show flaws in your technique.
If you want to end up with something, just make a plain cue using decent woods. There are a lot of woods you can get relatively inexpensively that will make a fine looking cue.
I don't intend to demean, but it just doesn't make sense to me to put any time into garbage. At best you will end up with better looking garbage. At worst you end up with garbage that is associated with you.
I'm looking at this project like this: It will take time and effort to refinish this cue. I wouldn't sell a cue that has points that are off by 3/4"--I don't want to be known for that. I wouldn't give the cue away--again, I don't want to be known for that. I wouldn't keep the cue in my pool room--you guessed it, I wouldn't want to be known for that. So, in my world, I would be looking at putting time and effort into something I would throw away.
If you want to learn something from this cue, dissect it. Find out what the maker did right (I'm guessing there isn't much), find out what they did wrong.