Staying within the original remit of the question and accepting the basic troop disbursements remain unchanged, then very little can be done to influence the potential outcome of the battle and as already been stated, Lee's mind was made up and he wouldn't be swayed.
However perhaps the only thing he might have been persuaded on would've been to shorten the line somewhat and use those troops as a reserve/2nd line and try to deploy skirmishers of sorts to protect the flanks.
One aspect that has been mentioned several times is the comparison to Napoleonic tactics and would a cavalry charge bringing up the rear made a difference. The answer to that point is possibly, if Stuart was available with most or all of his command it 'could' have made a difference on Picketts charge, that is presuming that most of the Union defenders could be kept occupied so Stuart wouldn't take to much fire and that is where the Confederate artillery would've needed to have been giving maximum covering fire, but anything less than a massive concentration would have been useless.
Yes French or Russian Nap cavalry possibly could've carried the positions on their own, but you have to understand that the mindset had changed significantly since 1815 and whereas cavalry of that period expected to make charges like that on a regular basis, during the ACW they generally did not. Infantry tactics whilst overtly looked similar between the two periods in reality they differed significantly, as we know this was mostly due to the improvement of weaponry that largely made Napoleonic tactics obsolete, even though Picketts charge was essentially just that, but without significant skirmish cover, light cavalry screens and heavy infantry reserves.
The other thing to bear in mind is that when making full frontal assaults, the attacking force needs to have a numerical superiority over the defenders, also taking into account distance traveled, otherwise it is usually doomed to failure.