Will 318, 340 or 360 heads fit on a 273?

Flip the heads upside down with the valves up.
Open chambers will have a big round "open" design that the piston can pop into quite far without hitting anything. Whereas
a closed chamber will not allow the piston to enter it at all, as there is a big wedge of material on the one side of the valves.
The open chamber heads could have a capacity to hold as much as ~72cc of water, whereas the closed-type comes in at 57 to 60cc
For a normally-aspirated 273, forget any open chamber big-port heads.

A stock-bore 273 has a swept volume of ~562cc. Even if you install flat-tops at zero-deck and an .039 gasket, the TCV (total chamber volume), with uncut open-chamber heads might total 80cc and your Scr will be in the basement at 7.95; that's at zero deck, which you would have to make happen. More likely, without decking, the TCV might come in at 90cc, dropping your Scr to 7.2 like Toolman said; hopelessly inadequate for anything but supercharging
Whereas;
with closed chambers of 57cc and pistons down .057 in the holes, she might make 8.7. That you can work with.
BTW
AFAIK all 318 heads will bolt onto all 273s. The angle error talked about is in the bolt angles that draw the intake down. The older heads are set up for the older intakes, and vice versa. IIRC the change happened in 66. There is nothing inherently wrong with the bolt angle, except 4bbl intakes are hard to find. The bolts are in the same place, and I have heard that some guys have modded their late intakes to fit on early heads.
You can install the newer 318 closed-chamber heads circa 1966/67,on your 273 as long as you also bring along any later matching intake. But I think 318 heads are spec'ed at 60cc, versus 273s at 57cc; I think.
AFAIK all 273/318 heads were closed chamber up to 67. (or maybe 68). And
AFAIK all 273/318 heads had the same valve sizes of 1.78/1.50 ..