Trying to create negative space within shape

[Anonymous]

Hi everyone, 

I'm currently stuck on a solution to creating negative space or removing a certain area from a shape. I've attached some sketches to explain what I'm trying to accomplish. 

Currently I've been trying to create a sketch with the outline, and then projecting it onto the shape where I can then start to attempt at removing space from the body. You can see on the stretched sphere to the right of the shape an idea of this. 

Basically, I'm having issues even getting the projected drawing, using split face, onto the main drawing (the flame). My idea is that it's because when I'm in model mode, the flame turns into larger faces with no splines, while the stretched sphere still includes more faces/splines. 

If anyone has ideas on how I can solve this split faces issue that'd be great. 

Even better: If someone understands what I'm trying to do according to my drawing, I'd appreciate any ideas or guidance on how to go about doing this. 

Here's a link to the file: https://a360.co/2SzIUMI

Thanks!

[jasonhomrighaus]

I have to admit to being a bit mystified when i tried to compare your sketch to what you had going on in your model.  I have perhaps guessed incorrectly in assuming you were trying to make some sort of mold.  If that's so i have attached your modified model for you to look at it is essentially that you position the models as you want them then Combine them using a cut which removes the tool body from the target.  I then split it open for viewing.   If this wasn't what you had in mind perhaps you could better explain what you are trying to accomplish as your end goal.  What is it you want to end up with.