You shouldn't need two health talismans on The Nomad. Just use one on the mandatory green spot and replace the other with a random red talisman. You could put it on your Rocket Dog if needed.
While you don't have any shield ability, you do have The Nomad who can give vanish to the team with his power ability (Mirage). Remember that Soldier Eddie can gain fury with two different moves, helping The Nomad to do Mirage more often.
A good way to get forward is to try to get some good troopers to pull out when you find a level too hard. Go for characters like Warrior Troll, Warrior Golden Son, Assassin Golden Son, Alliance General, Angel of Fear and Corrupt General. If you use troopers to get forward, you can focus your resources on upgrading the characters you already have.
I have a Soldier Eddie with the same talisman setup as you, and a team with him, my Nomad and a Rocked Dog from my troopers can easily autofarm Game of Death on Madness.