My friend is a triplet, now in her mid-20s, and she and her siblings are named Jack, Katy, and Lucy. Their parents chose names that each had 4 letters and were alphabetical - it's a nice connection but I personally don't think their names are too matchy. The other set of triplets I know (also in their 20s now) are named Karen, Robert, and Sarah.
I really adore your taste in names and honestly think you've listed very sensible choices. I am sure whichever you choose will serve your children well later in life. I really like a lot of them. Good, solid names. Pick names the 3 you like the best and that you feel suit your children.
I do like the idea of the triplets' names matching but NOT being matchy. With that caveat, I like (for example):
Arthur, George and Phoebe (all 6 letters)
Henry, Iris and Jasper (HIJ - consecutive in the alphabet)
Rupert, Sylvia and Theodore (RST - as above)
My favourite names on your list are: Rupert, Wilfred, Hugo, Theodore, Arthur, Jasper, Lawrence, Esther, Juliet, Iris, Martha, Beatrice, Phoebe, Anna and Violet.
Jasper, Rupert and Martha sounds lovely to me. I like Hugo and Iris together but I would suggest picking another 4 letter name if you were to choose those - but not Euan as it's too similar in sound to Hugo. Maybe you could pick Wilfred - nickname Wilf - so you could have a Hugo, an Iris and a Wilf. Lawrence, Esther and Wilfred also sound nice together - similar style but different sounds.
You could do something like this so the next name starts with the first letter of the last for a more subtle connection: Victor, Rufus and Sadie or George, Euan and Nora or Theodore, Esther and Rufus.
I quite like the idea of using individual names with the same meaning too: Asher, Felix and Beatrice/Gwyneth/Hilary all mean happy. There are quite a lot of names that mean peace so you could have a Callum, Frederick, Geoffrey, Humphrey, Jonah, Milo, Oliver, Soloman or a Wilfred and a Frieda, Irene, Jemima, Olivia, Paloma, Serena and a Winifred, for instance.