Given that I try to make lots of it, I've found what I think is the easiest method for extracting the juice from the tomatoes. When I'm processing tomatoes for canning, I remove half or more of the resulting juice. That's it!--no Foley mill or Saucemaster necessary. There's always plenty of juice left to surround the tomato pieces in the jar.
To be a little more specific; after coring and peeling the tomatoes, I put them in a big pan and break them up into inch-size pieces with my hands. (Thin rubber gloves work well for this.) I then strain out the juice, adding enough back into the tomatoes for canning them--usually 1/3 to 1/2 of the juice. I heat the juice and pour it into quart jars; then add lemon juice and salt and process them in a boiling water for 15 minutes. From a 30# box of tomatoes, I usually get at least 4 quarts of juice.
"Make mine tomato juice, please" (wink)