You should still be able to get sharp shots without MFA unless there is a significant mismatch between the body and the lens. If that is the case, you can always have the lens calibrated to match the body, which does the same thing as MFA but needs to be sent in to be done by a technician, rather than doing it yourself.
People were getting sharp shots before MFA became available, I myself used a 20D for several years and got sharp shots from it with all my lenses, with the exception of the 28-135mm (which wasn't a good lens) and that was solved by replacing it with a 24-105L which sharpened things up nicely.
I see that you list the 75-300 amongst your lenses, that has a reputation for being one of the worst lenses Canon have made, and is likely to be soft unless stopped down to a small aperture, MFA would be of no help there. Replacing it with ANY 70-200 should show an improvement in quality.
As mentioned above, there are many, many possible causes for shots to be slightly soft though, so it is as much down to good technique as good glass. I have had three bodies without MFA, and have several lenses and got sharp results from all (apart from the 28-135) so MFA isn't a necessity. Indeed, I now have a body which DOES have MFA, yet I have never felt a need to fiddle with it. I'm not saying that there aren't combinations of individual bodies and lenses that don't work well together, and can be improved with MFA, or even cases where MFA has been useful on all a photographers lenses (perhaps the body was at the edge of tolerance in one direction and there lenses were all centred or on the other side). What I am saying is that lack of MFA shouldn't mean that you can't get sharp shots.