Thanks for the tip, but on my setup it didn't work.

Browsing the shares didn't work - the server root appeared in each share root.

This implies that browsing the server root worked well - all shares were shown correctly there.

Instead of trying to solve the problem in the script, I just added one line for each share in the auto.SERVER like so:

SHARE1 -fstype=smbfs,username=USERNAME,password=PASSWORD,uid=1000,gid=1000 ://SERVER/SHARE1

SHARE2 -fstype=smbfs,username=USERNAME,password=PASSWORD,uid=1000,gid=1000 ://SERVER/SHARE2

SHARE3 .. ://SERVER/SHARE3

...

And so on.

That worked!