Sure, I rebuilt a few (always horizontally) until i got one going real good. After the last one i made worked out I've just been rewicking it when i need to.
The problem you are going to encounter is the ring of cotton which blocks the
juice ports. If you fully disassemble the coil and remove this ring you will find only two of the
juice ports will go straight through to the other side while the other two are seemingly blocked by a metal plate.
So what i suggest is to remove the vertical coil and its filler material but to leave the cotton ring where it's at.
Also keep that mesh screen but put it aside for now.
It helps stop spit back a lot
Take a pin and find your two "through" juice holes
Take a torch or lighter and torch those holes to open them (if you try to poke them out you will just mess it up) but leave the plated holes cotton intact.
Wind a coil of your choice but make sure it's not too wide or it will short out when you fire it. I like 5 wraps of 26g or 5 wraps of twisted 28g. (3mm screwdriver or coil jig is best to wrap on because of the juice porting)
Leave both your leads pretty long (make one longer, this will be the positive lead) and bend the positive inwards a bit as to keep it from touching the inside of the housing or you will end up shorting out..
Slip the coil in through the base until it's even with the juice ports.
Slide your 3mm screwdriver through the juice port and coil to hold it in place.
the shorter lead directly touches the coil base and rubber stopper goes over that.
Your longer lead goes between that stopper and the metal pin.
Clip your leads suuuuper short once its all together so that you can't even see them.
Wick it up! Not too tight, well you know the drill...
Clip down the wick until its pretty close to flush with the juice port.
Put the mesh screen back on top
Annnd you're done. Unless you didn't bend that positive lead enough to avoid shorting out!