You don't need to be "up" from your basic winnings for the Serendipitous trophy, you just need to have won more than 7777 coins within a single session within the casino. Meaning that you can take a break and go and buy more coins and it won't affect your ongoing tally, just don't go back to the HC.
All wins count. Not just Jackpots, I know this because I got my trophy immediately following a small win.
This is why Victory/Super Victory Mode are vital, because the coin return is scaled up across the board.
The reel spins aren't totally random either. For instance if you manually feed the machine and stop the reels in the order middle-right-left you'll get the same combination over and over, interspersed with the occasional small win.
More usefully, in auto-mode you can effectively "lock" the leftmost reel by keeping the autoplay held down. Basically spin the reels with pauses inbetween until you get a combination that looks nice (moogle on middle, 7 on lowest row is a good one), then keep the button down and that same combinbation will repeatedly drop on there for a number of subsequent spins.
If something else drops in, simply go back to stop-starting until you get the wanted combo again, then keep the button held down to restore the "lock".
There are videos on Youtube showing this, and I can confirm that it works exactly as described on PS3 at least.
Oh yeah, and obviously only ever play after the attendant tells you the machine's mood is "hot as a summer's day". If you get "on Fire" ask again until you get it.