Hi mate welcome to S.O.C
You could try Molyslip but doubt it will help as you rightly said sounds like the Synchro has worn. mines on its way it give a bit of a crunch into 4th :( you can have them rebuilt but as Pete said cheaper in the long run to get a 2nd hand one. As for the oil it can vary a lot but would recommend Motul gear 300 75w-90 or give our fellow friends a try at OpieOils get club discount too :) They can advice maybe with a cheaper or one that will help slip better on worn parts.
And love the idea you are doing with the your friends. Tlag his Son Bips and Adam on here do that sorta thing looks amazing. So please feel free to share any pictures or videos of your adventures. And feel free to join in on the forums, friendly bunch and not all just car talk. :D