Q:

How should I proceed after hours of not finding balance in this design?

Problem / Question:
I designed a logo for a little project I just began contributing on, but there's a problem:

The F was unbalanced, meaning there was no way I could use this logo on rectangular button or shape. Ultimately the balance makes it a poorly designed logo.
I've been working for hours to balance this thing, but I simply cannot figure out how to create an "F" that is balanced with the "I" & "X" using the style shown here (this is horrid):

Is there any way that I can achieve symmetric balance with the letter F in this style?
How should I proceed after hours of not finding balance in this design?

Result after building upon advice here:

Note: I'm still not liking the balance / shape that I've achieved. I'll keep trying.

Thanks to everyone who helped here, and feel free to chime in in the future with advice that might help others with this kind of problem.

This is posted as an answer, but just to make sure everyone sees it:
I think the lesson I learned from this may benefit others in the future:
When it just isn't working, try re-thinking your design.
Sometimes it's good to just play it simple. Although the simplest solutions can often be the hardest to reach: 

While this isn't related to the question directly, it's indirectly important: I kept working a design that didn't seem to want to be what I needed. 
In the end the answer was to revisit my objective and ask: Am I trying to create something because I like the style, or because it's the right style for the job at hand?
The answer was obvious in this case.

A:

Can you use one of the front slash line from the x letter and work something out with that? It could give the logo a nice flow. My suggestion is a 5 minute work with bad proportions, but it might give you an idea of something....

A:

I think the lesson I learned from this may benefit others in the future:
When it just isn't working, try re-thinking your design.
Sometimes it's good to just play it simple. Although the simplest solutions can often be the hardest to reach: 

While this isn't related to the question directly, it's indirectly important: I kept working a design that didn't seem to want to be what I needed. 
In the end the answer was to revisit my objective and ask: Am I trying to create something because I like the style, or because it's the right style for the job at hand?
The answer was obvious in this case.

