I think you completely misunderstand how full frame works.
A 17-55mm f/2.8 IS lens, will deliver identical geometry to a 27-88mm f/4.48 IS
lens on full frame.
depth of field is a function of geometry.
So as the iris or aperture opens up more it allows more light in, but because that light is light that is coming at a higher incident angle it is focused over a greater area if it is behind or infront of the focal plane. So therefore you have a shallower depth of field. See how the red point is larger and therefore will be blurred on the open aperture example?
Here's another example:
People have been misled with crop to full frame conversions for years.
The "35mm equivalent" is what is really important and nothing else. Your images on 35mm equivalent will always look the same no matter what.
From a physics perspective the "35mm equivalent" is capturing identical information. What really matters is the geometry of the light hitting the sensor, and with 35mm equivalent the geometry will always be the same for a given equivalence. Not only that but your flash settings etc will be identical:
Going back to the 35mm equivalent discussion, consider this:
On 7D compared the the 5D Mark III
The sensor is 1.6 x 1.6 times smaller.
35mm equivalent aperture - Multiply F-Number by (1.6 ) . (an f stop is a base 2 log, so even though we have 1.6x1.6 times as much light we take the square root, which is 1.6 to multiply the F number by. (example 2.8 x 1.6 = 4.48, 4.0 x 1.6 = 6.4))
35mm equivalent focal length - Multiply by 1.6
35mm equivalent ISO or light sensitivity - Multiply by (1.6 x 1.6) (bet you haven't heard of that, but if you do the math the 7D's sensor amplifies the signal 1.6x1.6 times more at a given ISO than the 5D3, so even if both say ISO 800, ISO 800 on the 7D is multiplying the pixels the same as ISO 2000 on the 5D Mark III)
The point is that people are often misled by manufacturers changing the geometry of a camera system, particularly putting in small sensors and then claiming otherwise impressive performance numbers which are incredibly misleading because you are measuring them on a different scale.
It's like saying:
I have a million dollars, and then failing to mention these are Zimbabwe dollars worth $20 not, American dollars.
Yes aperture ISO and focal length are fixed numbers, but so are monetary figures, and the most important thing even the most basic dealing of currency has is WHAT currency you're dealing with, and 99% of people require an "equivalent" frame of refference to understand foreign currency or need to do a conversion. Likewise with cameras, geometry (type of currency) is the most important thing when dealing with the performance of a camera system, and the first thing anyone needs to do is bring up a conversion to the local frame of reference, APS-C 35mm, whatever.
To respond to your concern though, there is NO benefit to a 1 stop faster aperture on APS-C sensor vs full frame because they (more than) cancel each other out. You don't stop action any quicker at all, whatsoever, because remember the ISO is skewed too, so all you're doing is just turning up the ISO sensitivity in a roundabout way by. You have been misled into thinking there is anything else going on.
Anyways, get the 24-105mm f/4.0, it will be much better in every way than your 27-88mm f/4.48 IS equivalent lens. Also remember ISO 800 on the 7D is equivalent to ISO 2000 on the 5DIII.
So in other words theoretically a Crop set to:
#1. 17mm - f/2.8 - ISO 800 - 1/50th - with 1/4 flash
#2. 55mm - f/2.8 - ISO 800 - 1/50th - with 1/2 flash
Will produce a 100% identical image with no difference in exposure, lighting, depth of field, field of view or composition when compared to a full frame set to:
#1. 27mm - f/4.48 - ISO 2048 - 1/50th - with 1/4 flash
#2. 88mm - f/4.48 - ISO 2048 - 1/50th - with 1/2 flash
Literally no difference.
Now of course each lens will have it's own characteristics and each body will likewise have it's own, and the full frame with the 24-105mm will delivery much better image quality as will any full frame body, but if both bodies and lenses were theoretically perfect and had the same resolution these settings would deliver the exact same with completely identical pixels.