I presume you are talking about tranny and premix? You don't say, but clutches and 24:1 aren't related too much.
If you had clutch slipping problems before, there was some other problem...like using 'gas saver' oil or somesuch. The kdx runs just fine on regular motor oil.
Use gear oil if you like. It's your bike.
If the previous owner knows it was synthetic, but doesn't know what it was...then it's doubtful he 'knows' it was synthetic.
It's a good idea to keep it the same as it was, though.
24:1?
What was the thinking behind that? Well, the more oil-per-gallon, the more power, but at some point it gets ridiculous. Kawi rec is 32:1. No reason 40:1 isn't just fine. You will likely hear from the amsoil 100:1 crowd...better them than me.
Asking 'which oil' is a waste of time. Everyone uses what is 'best' and if you don't use the same thing..there must be something wrong with you.
Point is, yanno...opinions and all..everyone has one.
Since you asked.......
I use valvoline motor oil in the tranny 30w winter/40w summer. Maxim SuperM @ 40:1
That's my opinion. Of course, if you don't run the exact same thing...there must be something wrong with you! ;)