If the 70-200 doesn't work for you, by all means feel free to sell it off and put the money toward something else.
Personally 70-200 is one of my most used lenses.... so much so that I have two - 70-200/4 IS and 70-200/2.8 IS "Mark I". I don't understand the limitations you are finding with your lens... I use the f4 lens all the time in covered equestrian arenas, which are considerably darker than overcast days, and f4 is no problem at all. I just bump up my ISO to compensate.
70-200/4 IS lens at f/4 and 135mm, 7D at ISO 800, 1/640 shutter speed, handheld, available light.
Within the last month, I've shot 12,000 images, many of which were with that lens.
But I'm not you and you're not me, so your needs and wants are bound to be different.
However, considering the limitations you find with the 70-200 f/4 lens now, I sure wouldn't go adding another f/4 lens like the 24-105. It would be heavily redundant with your other lenses, anyway.
You might want to check out the 135/2L, instead, if you need more telephoto reach than your 85mm offers.
IMO, the 135/2 is a "dream lens" on full frame. But it's also excellent on a crop camera such as your 60D (or my 50D in this case)... Here stopped down to f8 for depth of field:
Or used with a larger aperture to give a stronger background blur, here relatively close and at f4 (on 7D)...
And it's quite fast focusing, fully capable of sports/wildlife and other action photography (f5 on 7D)...
The 135/2L also works very well with a quality 1.4X teleconverter, for a 189mm f2.8, if even more reach is needed.
If the 135/2L is "too much" in any way, an alternative is the EF 100/2.0 (not the macro lens, though that's yet another option, just slower focusing and f2.8 instead of f2.0).
The 10-18mm (or an EF-S 10-22mm) makes a lot of sense to add to your kit, if you'll find uses for a wide angle lens.
Most think the Sigma 17-50/2.8 is a pretty decent lens. I haven't used it. But if you want something better, one of the very best in this range is the Canon EF-S 17-55/2.8 IS USM. An alternative that goes a bit wider (in case you don't get one of the ultrawides that go to 10mm) is the EF-S 15-85 IS USM. This also has superb image quality and an excellent range of focal lengths for a walk-around lens, but since it's an f3.5-5.6 lens might be best if you have two or three fast primes, too.
If you shoot a lot of low light/available light, you also might want to consider some other fairly fast primes such as the 50/1.4 and 28/1.8. These are smaller and less intrusive than many of the zooms, too, which can be nice for candid shots & street photography.