I use straps on shrugs so I can do it double over hand (hands facing towards you). My working weights for shrugs are around 140-150 just now but I struggle with DOH by around 120. I'm not convinced mixed grip shrugs is good for even trap training.
I wouldn't use straps on deadlifts though because that's part defeating the purpose. Just use mixed grip or learn to do hook grip, they are you're only real solutions long term. If you deadlift DOH then grip will always be your limiting factor so you don't be using the lift to best effect.
I think the best grip training is holding heavy stuff. Farmers handles are ideal but most gyms don't have them but a trap bar is second best, DBs third. I do holds after my shrug set where I just hold the whatever weight is on the bar for as long as I can.
Do grip stuff after deadlifts because otherwise you are weakening your grip by tiring out the muscles already. If you can do that many reps with the gripper thingy then it's far too easy, you are working on high volume endurance which isn't what you do when deadlifting.