There isn't really enough information on the MSTP configuration parameters to tell exactly.
However, unless it's really necessary (e.g. for security) I would have all the VLANs on all the links between switches. Manage load balancing with the instance tree priorities.
Suppose you start with where you ended up, with no direction connection between switch 1 and switch 3. Everything works fine.
Now you connect Vlan 6, so you have a loop. What MSTP might do, is to block the link between switch 2 and switch 4. Now you have connectivity on Vlan 6 only.