Leviathan keeps losing

Speed of a character is irrelevant in ships.  Other criteria determines ship speeds and turn order.  If both DRs and Levis are maxed out, then it's a coin flip.

Also, bring out Scimitar as your first reinforcement to give you a speed boost, don't worry if your hangars have been sabotaged, the speed boost stays even if it blows up.

Ships have their own speeds which you really can't influence.  max out your pilots and commander with 6* mods, all abilities maxed out, and as high a relic as you can afford.  you may get 3 additional speed.  

6 dot mods have the same impact on ship speed regardless of what colour they are. Taking them all to 6A is a huge waste of resources if you’re only doing it for ship speed. 

As ScoundrelRui01 said, run Scimitar. You should never lose running Fury-class, B-28, TIE Dagger with Mark VI and Scimitar as your only reinforcements and 6 dot mods on all crew members. Opening first turn is irrelevant. Hit Levis two specials, bring in Scimitar as first reinf., take out enemy B-28 with your Mark VI basic when it arrives as reinf., target enemy Dagger, hit full auto, win the battle. It's a painfully boring fight, but you will never lose a mirror match. Even with the odd AI enemy pulling in an early reinf. and/or the enemy taking out my Dagger, this strategy has failed exactly 0 times.

They really need to build a counter for it, or nerf Leviathan.