It seems to me if your E350/E450 has a stable front end you will not notice the play in the towing mechanism. Least wise, a stable front end will easily cope with a loose tow insert..
The first measurement you can take to determine if you have a stable front end is where the front end +caster is set. Ford ships these E series with the caster set at about +3 to +4 degrees which is OK for city driving BUT you want to have +5 to +6 degrees for highway driving. Just saying....