Carter has been on and off my list for a while, currently it's off but I do like it. I prefer Carson though. I like Jed as a nickname for Jedidiah, also what about Judd? Preston's not my cup of tea, Peyton maybe? I can't take Maximus seriously, I think of it as a dog's name, or a horse, just Max? Or the French Maxime maybe? The look of Roan confuses me, I'm not sure how to pronounce it. Rowan? Ronan? I prefer the fully Jacob to Jake. Also really like Jacoby (I pronounce it Jack-o-bee). Adam's recently flitted under my radar, I like it, but not enough to put on my list. Some other ideas: Axel, Quinn, Keton / Keaton, Sullivan, Presley, Xander / Zander, Fenton, Jacques, Koby, Cody? :)
I like Carter but it is so popular now that it has lost the appeal. Cameron, Parker or Sayer are much better in this case.
From your list I just love Adam(love it in general and Bible&Shakespear connection), Preston and Jed. What about Jared nn Jed, Jacoby nn Jake, Maxwell, Vincent, Calvin, Cruz or Theodore?
I'm not a big fan of Carter. It's so common these days that you can be sure there will be a number of Carters in his elementary school class. From your list, I personally love Roman. It's classy and masculine, but also not extremely common. Jed is nice, usually short for Jedediah, but I don't think it has the same sophistication as Roman. Preston is nice, but very preppy.
Other suggestions: Simon, Asher, Collin, Callum, Declan, Conley, Finley, Damien, Dominic, Graham, Grant, Cole, Kirk, Kent, Keaton, Stanton, Rhys, Reid, Tristan, Travis, Forrest, Eli, Elias, Elijah, Emmett, Everett, Jude, Jasper, Julian, Jefferson, Jameson, Nolan, Harrison, Heath, Caspian, Hudson, Casper, Allen, Porter, Ian, Caleb, Isaac, Ewan, Cavan, Lars, Lance, Leif, Levi, Lucas, Luke, Mark, Marshall, Marcus, Mitchell, Miles, Malcolm, Orion, Oskar, Orrin, Dallin, Talon, Quentin, Quincy, Ross, Roscoe, Seth, Stanley, Samuel, Thomas, Victor, Vincent, Wendall, Wesley, Whitman, Edison, Wilder, Easton, Eastman, Xavier, Zane, Josiah, Judah,
The trouble with a lot of occupational names for me is that I hear them differently than some people. For example, Carter sounds like "cart her", Rider/Ryder sounds like "ride her , Hunter as "hunt her"...well, you get the picture! :) Surnames of former US Presidents are super trendy and I would avoid them like the plague. Roman makes me think of felon Roman Polanski so that name holds little appeal for me. Jed and Jake need their full names. Maximus is too heavy on the macho swagger. From your list, I like Adam the best with Preston coming in second place.
Carter is a little popular for my taste but it is a nice name and I see it's appeal. If it's what you love though don't let it's popularity disuade you. I'm all for going with your heart when it comes to names!