Black Hand is exactly right that for Eastern Center Seam Moc's, you need soft and supple leather to make them correctly.
My apology that I did not think of Moose hide to suggest, as that wasn't available in my neck of the woods during the time period Eastern Moc's were made. So when I think of leather for these Moc's, I think Elk or Bison as most Deer skin available is garment weight thickness and that's too thin to last very long for Moc's. If you go with Moose Hide, you will still need it soft and supple, so around 5 to maybe 6 oz weight is going to be preferred, except for thicker leather for an added sole you may wish to sew on the bottoms.
Since I am also concerned with making things as historically correct as one can and still afford the leather to make things, I stay far away from machine grain impressed leather for Moc's, Shooting Bags, etc. This because while there were some kinds of impressed leather in the 18th and early 19th century, it looked quite different than what is available today, unless it is custom tanned/finished. I admit I don't use real brain tan leather most of the time as it is too expensive nowadays, though.
Don't get me wrong, I have been going to the Tandy Store here in Richmond, VA since the mid 70's and have "chased" them to the different locations they moved to over the years. But for some things, you just can't get the leather you need from Tandy for some projects.
Gus