Knowing I would one day go full frame - and did, 2 years ago - when I started replacing my EF-S lenses, a 24-105 f4L was my first purchase, followed by a 16-35 f2.8L ii for 'wider' shots. A year later, I bought a 24-70 f2.8L i but didn't like it because it lacked IS and was just plain too heavy on my 60D. So it was gone in less than 3 months.
I couldn't be happier with the 24-105. It's the lens that's on my camera 70% or more of the time...and on the 60D when I had that, too. And, as Derrel indicated, there's many 24-105 Ls available used as well as new white-box from kits, all at a good price. When buying used, other than 'mint like' appearance and clear glass, I look very hard at the contacts. To me, that will tell how many times the lens has been on and off a camera.
My current lens lineup is 16-35L, 24-105L, 80-200L, and 135L, all Canon. High on my list of zoom lens criteria is overlapping zoom ranges. While the 24-70 is an outstanding lens, even the mark i, with a 70-200 to go with it, I envision too many times when the 24-70 is mounted and you want to zoom in to about 80-90 mm, so you have to move closer or switch lenses. Having the 24-105 avoids that problem.
Many here and elsewhere complain that f4 is too slow, or the 24-105 isn't sharp enough. The only time I found the f4 too slow was low light work and I had to shoot at ISO 3200 on my 60D, and I was STILL in 1/10-1/40 shutter speed territory. So I had to take about 20 shots from a monopod to get one with zero subject movement. So be it. The 5Diii cured the ISO problem. Others are concerned with its sharpness. Once I performed MFA on it on the 5Diii, I'd say it's a match for the 70-200 mark i in IQ. So no complaints from me whatsoever.
Would a 3rd party 24-105 or something similar work for the OP? Probably so. Performing MFA might be a little more complicated, but shouldn't present any problems.
