Too bad your 2002 tranny is not coarse, since many are. I don't know when BMW went to the fine spline flanges.

Things you can do:

1.Get another 2002 tranny, but with coarse spline.
2.modify your existing driveshaft.
*3 Now, there is one little known thing you can do that an old school 02 freekazoid like mewould know about.
The 68 2002 also came with a longneck diff and a driveshaft with telescopic center like that of a 1600.
This driveshaft is similar to your 68 1600 driveshaft, but is different because it uses u-joint amidship and rear instead of the rubber guibos of your 1600 driveshaft. And most importantly, it mates to the 4 hole flange of the 2002 both at the tranny and rear. This means you can keep your fine spline trany and 4 hole flange and simply mate them, but you would have to remove your diff and replace the 3 hole flange on it with a 4 hole. The 4 hole is found on the
68 2002 longneck 3.64 diff. This flange swap is permissible on the longneck diffs only due to their design. While you're at it change the seal. 3.64 longnecks though are getting kind of sparse.
***Another alternative would be to only use the front section from the 68 2002 driveshaft and simply push it into the rear section of the 1600 driveshaft. It fits,but you will probably have to take your new driveshaft combination to get it balanced. Swaping sections between 1600 to 1600 does not require rebalancing, but the 68 2002 sections are balanced together (something to do with the u-joints vs. rubber guibos). That is why their corresponding sections are numbered and the 1600 sections are not.
This would be your cheapest alternative. Just swap out the first section of your driveshaft with that of the 68 2002. If you get vibration, take the entire drivesaft off and get it balanced. You will have a 4 hole guibo at the tranny, a u-joint amidship, and a 3 hole 1600 guibo between the driveshaft and your diff.

The 68 2002 driveshaft is the best 02 driveshaft made. It combines the strength of the 2002 driveshaft (U-joints)with the telescopic sliding section of the 1600 driveshaft. It was most likely discontinued because of unit cost of production. Similarly the longneck diff is superior. It holds more oil and cools better. Its design allows for seal replacement and flange swaps without having to disassemble the entire unit to replace the crush collar. It is also heavier and puts more weight at the rear axle where it is needed on our cars. It was also discontinued due to unit cost of production.

Now you can go and confuse the hell out of parts vendors with the info I gave you. To make it simple, just get a 68 2002 driveshaft Some of the guys on the board have them laying around.

Slavs