Here are a few options:

• https://deadwoodjedi.com/speed-tunes/myth-heir-with-no-seeker/ - needs Doomscreech
• https://deadwoodjedi.com/speed-tunes/budget-myth-heir/ - needs 2x Pain Keeper
• https://deadwoodjedi.com/speed-tunes/myth-deacon/ - doesn't need any additional pieces, but the speed requirements are quite high

Thanks. So for the unkillable teams to work, is my understanding that all I need to care about is to get the champs to the corresponding speeds.  I do understand that the DPS champ need to have high atk or acc to land poisons or debuffs. But does any amount of defence and high HP ok or do I still need to ensure that each champ has more 3.5k -4k defence and almost 40k HP

Basically, correct. The only caveat being, often there are setup turns, and you obviously need to survive that part.

Additionally no bad masteries.

Thanks. I understand..

If by no bad masteries, u mean those that deal with TM alteration, i havent chosen those as they might mess up the speed tunes.

The only one you are safe to take is Lore of Steel, as it isn't conditional. Any of the others, in particular Cycle of Revenge, are off the table.

Any of those and additionally usually any that do cooldown reductions are bad.  Generally only Cycle of Magic for UK teams that people would take.