I'm not sure why it would be the melee minions that you would be targeting with this change. Melee minions hold waves in place, while caster minions are what push down lanes. If the concern is AP champs getting minions pushed against them, it seems like adding damage against caster minions would be more helpful, but pushing minions seems like the least of the problems AP casters have.
As to the original post, magic damage is doing just fine in Dominion. Look at Kassadin, Warwick, Poppy, Lulu, AD Malz, etc. AP is where the problem is - it just happens that most AP damage is magic damage. AP just doesn't translate into damage anywhere near as well as AD, procs, magic pen, and base damage do, especially without Rabadon's. SR is balanced around mages with Rabadon's and blue buff, with them being able to front-load a lot of burst onto enemies that are generally squishy enough to care about that burst, then they can hang out for a bit and do it again later while holding behind the stronger towers and larger teams, but burst damage doesn't mean nearly as much in Dominion if you can't finish the job.
That's why what is needed is some source of sustained DPS that comes from AP. Don't limit the AP ratio to minions - give an auto-attack AP ratio against champions, even if it's in item form, like as a Malady upgrade.
EDIT: To put things more into perspective, at max CDR, Morgana gains just under 1 damage per second for every 3 AP she has. Sunfire Cape is considered a weak item for increasing your damage, but you would have to build over 120 AP to increase your dps by the same amount. So, for 2610 gold, you are getting roughly the equivalent of 3 Blasting Wands of dps (which costs 2580), plus all that armor and health. All this for what is generally considered a bad item.