Yep, I agree... use the algorithm to narrow it down (top 5)... then random draw as basically an admission that the formula isn't perfect and likely any one of these players is deserving for various reasons. Even in real life football there's often debate whether player A or player B should have won the Heisman or MVP or whatever... it's not just stats, but the level of competition (which is why elim/reducing blowout stats is good) and whether that player was a difference in helping his team win or if they still lost, just by "less than they would have", etc... so I think a random element in GLB world helps approximate all those "squishy" factors.
I don't know if team record is a factor in MVP, but I kinda think it should be... not necessarily that 14-2 team player gets an edge over 10-6 team player... but maybe just that there's a flat bonus for anyone on a team with a winning record (i.e. 16-0 = 9-7 for algorithm purposes). Makes it harder (but not impossible) for a team with 8-8 or losing record to have any MVPs, which I think is generally more realistic as to how those types of awards are given out. Just a thought, and probably a bit off-topic here.