So I found two hero-item pairings that've worked great so far. As I haven't seen these on guides before, I'm posting them here for feedback.

Karthus + Rylai's Scepter
-Lay waste slows for 35% = Caster's "Frozen Mallet"
-1 sec cooldown, spammable
-Defile slows for 15% = mini Nunu ult
-great HP for Karthus
-dunno how Ult is affected? (15% or 35%, on-cast or after-damage)

Heim + Innervating Locket
-normally Heim-players get Heal for turret clusters
-now rockets/ EMP heal turrets
-HP and mana = great buildup for fragile Heim

If you get a chance to test these out, let me know how they work for you.

Lay waste is aoe so it slows for 15%.

I'm normally a big fan of RoA, but some champs are better than others for it, and I'd suggest Archangels + Rylai's instead of dual RoA as a core for Karthus. Any slow is a good slow, and with that kind of ability spam and the horror that is Defile, he's a pretty good caster to build slows on.

Regarding the Requiem/Rylai question, I'm pretty certain the slow would occur on casting. It's how Rylai works on Cho - the Rylai slow occurs immediately in the area on cast when you fire off Rupture, even though the Rupture effect itself has a delay.