You can’t really sharpen it that much, as you say… but you can do things to convince the eye that it is seeing more detail than is really there.
Grab a ten second clip from the worst section of the video.
Now, duplicate that clip and stack it, make, I dunno, three identical tracks stacked vertically.
Park your play head somewhere in the center.
Now, you will need to change the blending modes of all tracks above the orignal one. Go to modify>composite mode. Use the 3-way color corrector effect on each track for a different effect. One track is for hyping the high end, another for mids, a third for the darks.
Play with changing each track’s composite mode, try screen and multiply… I don’t know, try everything, that’s what I do:-) …and adjust the opacity of each track to control how much of it’s quality is contributed to the whole. Use one track to color correct to push the bright details. A second one to concentrate on the detail in the darks. This may take hours, but the good news is, when the ten second sample looks good to you, select each track, one at a time, hit “copy”, then click on the rest of that track thru the whole video, right-click,and paste attributes on the appropriate check boxes, to apply what you’ve done, universally to each track in turn.
Or, spend weeks learning Apple Color:-)
Seriously, though, give this a try, what have you got to lose, except the wedding client and all the bad references they’ll make if you fail. No pressure.
You might also want to change the final video to progressive and not interlaced, as the temporal artifacting from that sometimes makes things seem sharper too.
Should you have a massive success, please do come back and report on it, maybe post a still of the before and after.