The first is simple. Just use the support from Bulgaria which Russia cannot cut.
Turkey: Fleet Black Sea -> Rumania.
Turkey: Army Bulgaria SUPPORT Fleet Black Sea -> Rumania.
Turkey: Army Armenia -> Sevastapol.
The main problem with this approach is that it is likely to give up the Black Sea, which will make it very hard to advance any further from this position.
The second solution is to convoy Armenia across the Black Sea to Rumania (this is the leapfrog attack again).
Turkey: Fleet Black Sea CONVOY Army Armenia -> Rumania.
Turkey: Army Bulgaria SUPPORT Army Armenia -> Rumania.
Turkey: Army Armenia -> Black Sea -> Rumania.
This is probably the best attack against the new Russian defense, but because it doesn't cut the possible support from Sevastapol it fails against both of our original Russia defenses.
If keeping all of this in your head makes you dizzy, then it's time to build the move resolution matrix:
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The Russian defenses have been listed by the key defensive order given to the Ukraine, while the Turkish attacks have been listed by the key attacking order which is being given support.
Can you fill in the results for each case?