Is there any way to play that map that was marked out for the tutorial but pick your own settlers?
Sure. Hit ESC from playing on that map and select "Export Local Image". Pick a floor or two and export them. There will be a file generated in your DF working directory that includes the worldgen parameters (just though recently created text files). Back at the DF starting screen, select "Create New World from Parameters" and give it the map seeds from that worldgen. You have now created the same world that TinyPirate
created. Finding the right starting location (out of all the possible locations on the world map) will be a bit harder, though. The site-finder might be able to find it if you specify YES and NO in all the correct fields, e.g. Magma Pipe = YES, Magma Pool = NO, Flux Stone = YES, but that's a gamble.
It's easier to make a copy of the folder your savegame is in (rename the folder "AbandonMe" or similar) and then load that game up, Abandon the Fortress, and try to start a new game in Reclaim mode. Reclaiming will show you where the fortress is on the world map. Use that information to go back to your newly-generated world and pick a starting location. Now select the dwarves you want for your embark and get to work! If there's a mix of dwarves and gear you really like, consider saving it as an embark profile.