I can definitely see where the F3 would be a great pick up! The only thing would be cost to get all that benefit.
$1000 - $1200 for a body
$$$ For PL lenses or $200 for an ef adapter
$230 per camera media
$600-800 for a recorder that supports raw
$100+ for SSDs for the Recorder

At that point, you could also swing for the FS700 with the 4k license. They run around $2300 for the body. You would also get super slow-mo, 4k Raw/ 4:4:4 formats, and s-log. You would get to keep the ND filters from the F3 as well as have a more versatile mount to put glass on. This would be a little bit pricier than an F3 but would be "future proof" in a sense that your resolution will be useful into the future.

Just my two cents on the cameras. Any of those choices mentioned by Marc or myself would be good options, but look at what you need ultimately.

I think a good option to look into would be a Sony FS100 if you want to get something that removes the BMPCC hang ups.
1. It has wonderful battery life with cheap battery options ($20 for off brand),
2. XLR on board
3. Good dynamic range and Super 35mm sensor. The Color profiles will need to be tweaked to match the BMPCC more closely, but this camera is older so there is lots of info on color profiles.
4. E-Mount Mirrorless mount which is great for adapting lenses to. I use canon EF for zooms and vintage Nikons for primes. Both are plentiful and affordable.
5. Price used is between $800-$1000 for a solid body only kit.
6. 1080p 60fp and internal slow motion.

There are some short comings on this camera such as the 8-bit codec and form factor can be odd. It does however provide a lot of quality for the price and would remove a lot of the BMPCC's weaknesses you mentioned. I shoot events, interviews, and music videos on mine and have loved it for the shear usability it offered over a DSLR-style camera. Just another option to think about, and my two cents.

I think I can give some insight but a couple questions first

What things are you filming in your travels?
Would you like slow motion?
Where do you travel?
Are you off in rural areas a lot?
Do you have lenses already?

I can see where you are coming from, but I can never justify the price of Apple's hardware and can't understand why they are always pushing sub par GPU's in their systems. FCPX may run extremely well on that platform but every other piece of software suffers due to their lack of higher spec'd hardware.

For those wondering Raw bitrate runs at 1 Gbps or 125 MB/s or 7.3 GB/min. Seems like Canon created their own 3:1 compression similar to BMD on the Ursa Mini Line.

John is right grab a monitor/recorder with loop through for SDI out, and enforce the kit fee. Think of this way. Your camera is a depreciating asset at some point you will need to replace/upgrade it. If all you ever do is charge for your time then you will be cutting into your earnings, and be stuck digging into your personal income to cover costs. We experience this everyday when we purchase food or any other items. Businesses figure in these costs all the time. Vincent Laforet put it into great perspective in this article.

http://blog.vincentlaforet.com/2013/08/01/how-to-succeed-as-a-creative-l...

Another point that I still struggle with at times is letting clients beat me up on price. When we lower our prices and do things at sub common rates then we actually hurt the industry as whole by creating a standard that clients will always go back too even with other service provider (cam ops, videographer, cinematographers, etc).

Client: "Well this guy/girl didn't charge for that."
Cinematographer: "Well that's not standard for me, these are my rates."
Client: "Your just gouging me on the price! I won't be recommending you to anyone!"

This problem already exists and I think we all have to work to alleviate this within our industry. Professional quality gear and work isn't cheap and I don't think we should have to suffer through the "It will look great on your reel" crap that is prevalent. Best of luck with your decision and standing up for what you (and your gear) are worth!