When you say you need a splash screen for your game. Any experienced developer, even gamers, should immediately thought of the LOGO display during start of the game. For programmers, they will think you want a bitmap to be displayed before the actual program runs.
But what you want seems like a transition screen (not really a splash screen if you set it up to calculate loading %).
The java example you show is indeed a splash screen, a dummy(fake) loading screen that does nothing but display a set of animation before transition.
As far as i know, the game allows you to pre-load certain scene before actually loading it during scene termination, but it's hardly noticeable with this type of game, so the time you go into a "loading scene" and out probably took longer than the pre-load to load.
The "time-gap" you found between each loading scene is actually a "forced" delay time on transition, which can be reduced to 0 for instance scene change (without the fade out and all).
For the Logos that run before the title screen, you can either make a new scene and rewire the game to point there before moving to title. a new class name Scene_Logo can be easily made.
As for the transition splash screen, you don't even need a script for it.
Simply set up a common event to fade out, display a picture and fade in. change the picture in between "wait" to animates it.
When that's done, add the common event to your area transition event and fade-in after that.
