New heads

What set of heads can I buy and bolt on and run? People have told me that any new heads have to be reworked before you can use them! And what would be the correct heads for a 318ci bored 30 thousands mild cam Tri headers 904 automatic! 69 Dart gt! Thanks
your question, as posed, is, IMO, as good as impossible to answer.

what are you expecting out of a head-swap?
How far down in the bores are the pistons?
Not a chance would I install any open-chamber head on a 1969 street 318, with an automatic.
So that leaves closed chamber heads.
and if you do that, then you have the Quench issue to deal with.
Alloy heads will cost you the equivalent of somewhere between one half and a full point of compression by virtue of their excellent ability to pull heat out of the chamber. Heat is power, so; this means that with a simple swap to alloy heads with no other changes, you are likely to lose ~4% power, everywhere in the rpm band from stall to peak power and over the nose. With 318 pistons usually down in the hole, you can't afford that. This power-loss will be most noticeable at lower rpms. which, unless you have racegears in the back, is gonna very noticeably soften the performance below 3000/3500 rpm.

The overbore helps nothing, unless, during the rebuild, the piston tops were sent to the top of the bores.
The shorties are a high-rpm design, but in all seriousness, for street, are only half a header, not being tuned for the rpm that most streeters drive in. But worse is that those shorties will pretty much kill the overlap period of any cam you install; so that also kills the top end power. So really, all they do is provide a clean place for the pistons to push the exhaust gasses into, which unless the throttles are wide open, is of almost no consequence.
At this point, the mild-cam, at sub 3500 rpm, may actually be costing you power. Alloy heads will just make it worse.

The 69 engines were rated at 9/1 Scr, which demands a total combustion chamber volume of no more than 81.5cc

IIRC the 1969 heads were about 60cc and the steel gasket at a tic over 4cc, for a total of say 64cc. that means the balance, 17.5cc comes from the shape of the piston tops and the deck volume. I'm pretty sure the 69 pistons were flat tops with no eyes, so that puts the pistons down at ~.089 I sortof remember the spec was .057/11.2cc, so the pistons must have the missing 6.3cc. It doesn't really matter, since the Quench is outta sight either way, between .077 and .109, both with closed-chamber heads. which just means this combo should not be detonation prone, at 9/1 Scr.
The thing is, the .020 headgasket is gonna be a special order, and the ones that come in the rebuild kit are like .057, and the fire-rings are like 4.18 inches in diameter for a net of 12.6cc as compared to the steel shim around 4cc. So if that gasket gets installed with flat top pistons .090 in the hole, this jumps the total chamber volume to 90.58@ plus .030, and the Scr becomes ~8.2 so, If you install 60cc alloy heads on a combo like that, then it will perform like 7.2Scr in most of the working range of the throttle openings, the rpm below the torque peak, and it will be severely hampered by a stock stall, and say the common 2.76gears of the day.
Now I know you didn't ask these questions, and for all I know your engine has been decked to ZERO, or close to it; But it seems to me, you wouldda mentioned it, cuz it is probably the most important part of any 318 street-build.
And you may have 4.10 gears and and a 3000 stall, IDK, but you didn't mention that either.

The point is that all of us are just pissing in the wind, cuz your question, as posed, is as good as, impossible to answer.