thomas, you can make the player walk to a position with a position compare condition and then set x velocity to the player walk speed.
Also, for the ledge jump not being powerful enough thing, you can hard-force a jump of any height either by
a: setting the player's jump strength to a higher number, jumping, then immediately setting it back within the same event
or more easily....
b: set the y velocity of the platform movement to a negative number (which is what "jump" does essentially)
by controlling the y velocity you can make any kind of jump sustain/ jump system you want, even add a manual sustain to second jumps like you want with a bit of eventing.