You could, pretty much any modern APS-C Canon will be an improvement over what you have. However, going FF is fantastic. Not sure how the 28-80 would hold up (the 24-105 as a 'kit' lens is actually pretty darn good, if you can afford the kit over body only), but as AmbientLight said, the 17-40 being 'bad' on FF is overblown. Yes, it has it's weaknesses, particularly in the corners at wide apertures, but it's a pretty capable lens. I've got one I use on my 5d3 and it's pretty nice. If anything, you'll be able to get bigger prints out of your current lenses, or same prints at a bit better quality.
Alternatively, you can always get some of the good non-L lenses such as the 40 f/2.8, 85 f/1.8, Sigma 35 f/1.4. Admittedly the Sigma 35mm might still be a bit out of what you can afford if you can't get the 6D + 24-105 kit, but the 40 f/2.8 is quite sharp and nice, the 85 f/1.8 is a quite good performer at that focal length. Or maybe you could look around for a 24-70 f/4 IS kit. It's a fairly good lens for what it is, although people really wanted it to be a f/2.8 or an updated 24-105, and so were a bit disappointed.