Yeah it sounds like you were just being too aggressive. With Malzahar you're not an initiator; if you're not just farming, then you're trying to pour on damage from a safe distance and essentially just scare them off unless and until an ally makes a serious move in. Then you use the dogpile as cover to dive into ulti range and lock down one of their critical specialists or secure a kill. When I see a malzahar with lots of deaths, it's usually because he was trying to initiate with his ultimate and got wrecked by all of the target's teammates. There's a reason tanks are usually the initiators.
Loved all the comics, want to see more.

And to clarify that thing about turrets:
Normally attack damage (ignoring crits) is (base attack damage + bonus attack damage), adjusted for armor factoring in armor entry. Bonus attack damage is any attack damage you get from runes, masteries, abilities, items... anything that boosts AD in any way.
When attacking a turret, armor pen is not counted. Additionally, if 40% of your AP is greater than your bonus attack damage (i.e. if your AP is 2.5x your bonus AD), then that 40% AP value is instead added to your base attack damage when attacking the turret. The damage is still mitigated by the turret's armor value and still doesn't count any kind of entry.
This was added because it would otherwise be way too easy to completely ignore solo APs pushing on your turrets. Having to recall to stop a solo pusher can be a pain in the butt and ruin your inhibitor attempt; if you can ignore them at all, you will. By making sure that AP champs can deal some decent damage to turrets in the mid- to late-game, they become more viable turret threats that actually need to be dealt with.
One curious effect of this either-or mechanic is that while AS+AP builds (popular on twisted fate, teemo, kayle, fizz, kog'maw) can deal some pretty decent damage to turrets, hybrid AD+AP champions won't deal nearly as much damage to turrets as you might expect them to, because they're only dealing the higher value of bonus AD vs. 40% AP, not both. This means that some hybrids can be worse at bringing down a tower quickly than some pure magic damage specialists, even though magic damage is supposedly specifically about killing players instead of towers.