I have done both; gotten the dent fixed and have also replaced a neck.
Personally I wouldn’t buy the tool because for a bit more money a repair guy can do it and probably better and faster than me.
There can be an advantage with a new neck because they can effect the tone. Mine is a pro selmer tho and so don’t know if the difference would show on the student model you have.
Why don’t you take it in and get a quote for them to do the repair and go from there.