For example, a navy battleship that costs three times as much as it's ordinary counterpart would only be as cost effective if it actually cleared missions three times as fast.

This is stupid.

What you're really asking is for the best level 4 non-fation t2 fit battleship, because this metric rules out basically everything else.

You will need to specify a time frame for this, mission long enough with anything and it becomes cost effective

Seconding that "you need to specify a time frame".

And generally speaking, the hull cost of most t1 Battleships are similar to each other.
Then using t2 BS's, Navy, or Pirate BS's are better under various situations.
Faction and deadspace modules are also ways you can improve your ships performance for a wide variety of pricing.

Are you expecting to pay for it in 30 hours of missioning? 100 hours of missioning? 500 hours of missioning?

Perhaps a better way of phrasing this would be:

Which missioning battleship & fit will give the fastest return on its cost from Level 4 missions?

Here's a challenge for the forum community: what do you think is the most COST EFFECTIVE battleship for running level 4 missions?

mission long enough with anything and it becomes cost effective

Unless it get attracts suicide gankers.

Well yes, which is why a CNR isn't always ideal, even less a Golem. You either best have your d-scan open, and/or have a second account char on grid with some appropriate counter measure fit. Or just do as I do and hop in a scorp to do missions now and then when things seem odd in your usual mission locations but need a BS for some reason (though often a cruiser is enough). But ravens are effective enough, not so much a high-profile target, affordable if lost. You just need to be aware of kill/pod activity in recent hours, who's operating in surrounding space, know your possible exit possibilities, watch for probes.

I thought the suicide gankers would scan your ship (or find some other way to get your fit) and assess if it's a profitable target first. Then gank it if it was worth hitting. So an expensive hull wouldn't make you a gank target if you weren't running expensive modules.

Well, unless you did something which let gankers hit you without having to worry about Concord.

Unless it get attracts suicide gankers.

A cruiser fit to speed run and we name it "a battleship"?
cha-ching!

Otherwise, raven? Fairly cheap to fit, easy enough to fly. Anything with range seems less risky for pve.

I've heard of running Level 4s in a BC, but never in a cruiser. I'm worried that anything without at least a BC's tank would get squashed by those few rooms that aggro you right away at close range.

I'm not looking for ISK/hour here, but ISK/hour/initial ISK invested. For example, a navy battleship that costs three times as much as it's ordinary counterpart would only be as cost effective if it actually cleared missions three times as fast.