Is there a way to prevent traffic from going to the link which is in Discarding on the other side?

Let's say I have two bridges connected with two links. They both have VLAN 200 in MSTI 2 and VLAN 300 in MSTI 3. Both of these MSTIs are assigned to the ports g0/1 and g0/2 on each bridge. Bridge A is the root and it has all of it's ports in Designated - Forwarding.

Now, let\s say that by the mac-address table, the path for the traffic from Bridge A to Bridge B in MSTI 2 is via g0/1, in MSTI - via g0/2. But if we have broadcast/unknown unicast traffic in MSTI 2, it's gonna utilise not only the g0/1 link, but also g0/2 (which is in Discarding for that MSTI on the side of Bridge B). Which means that we are gonna saturate g0/2 port with the traffic that's gonna be discarded anyway. Is there a way to prevent this situation from happening?