You can start off on the floor you were last on if you quit for the day. Going home doesn't reset your dungeon progress to floor 1, so don't sweat trying to power through it in one go.I'd like to, but I have no way to recover SP in a dungeon other than that right? Just in getting to level 7, I have to fight enough enemies to basically completely deplete everyones SP, and 6 soul drops or whatever does not get me out of that emergency.
If you are absolutely riding close to the deadline, and don't want to rewind back a week, you can use the SOS feature, though that requires other players be playing, and you can also find SP recovery items in chests. But the chance of success with those solutions is slim. As it stands, though, yeah, if you've run out of SP you'll just have to leave the dungeon to recover. If the guide disagrees, then the guide is wrong. A first timer shouldn't be beating these dungeons in one day, especially not the first dungeon, as you haven't got the full team yet, so you're not familiar enough with the game mechanics to optimise your strategy to get the most out of your SP reserves.
In short, following guides to the letter on your first play seems kind of foolish to me. I'd just use it as a very loose framework about what level you should be in what dungeon, and give you a basic idea of how long you have to beat each dungeon, what fusions you should do and so on. Following it day-by-day on a first run ruins the spontaneity of the game, in my view. I'd write off your losses in this dungeon, go home, recover your SP and take another stab at it in the next day. Do not throw away your SP recovery items on grinding through the dungeon in one day, because you may need them against a boss later in the game and, as you already noticed, they don't recover much...