Retune my entire carb after installing new heads?

The biggest cam I have tuned is the 292/292/108 in my 367. So what I'm about to say, may not apply to your combo. But I'll say it anyway, cuz you just never know.
I'll tell you what I think. not necessarily what I know.
As to the Idle-speed;
I think
27* of Idle-timing is conspiring to close your primary throttles too far, thus killing the transfer-fuel delivery, and I think this is causing the Mixture screws to have to opened too far, to get enough Idle fuel. The result, with a 4-corner system, is extra air getting inhaled thru the slightly open secondaries , and so the Idle-speed has to go up.
The above is what I think. I mean the air could be getting in there from other sources too....

Now here is what I know.
I know that your engine/ any engine, needs a certain amount of fuel to make enough power, to idle on. And I know it is normally supplied by a balance of transfer fuel plus mixture screw fuel. And that means, you can adjust either way for best results ..... at idle.

Theory
So then, you can increase fueling from the T-slots while simultaneously subtracting fuel from the mixture screws, This then maintains the fuel, while simultaneously subtracting air, from the secondary cracking screws. By doing this, you can also subtract Idle-timing, and then the idle speed will go down.
Now, the Ica on my 292 was between 70 to 74 degrees, which puts the piston well on the way up the bores on the compression stroke..... which means, at idle, some of that just inducted mixture is gonna be pushed back up into the intake which then causes the idle vacuum to run pretty low. Sooner or later it will get to be too low for the engine to continue running. For my combo, this occured at 500rpm in gear and pulling.

IDK
how low your idle-speed can go, or
how low you might want to go,
but idle-timing for those engines that I have tuned is not that big deal, at least, not nearly as important as getting the Idle air right.
For instance;
I had no problem setting the idle-timing on my 292-cammed 367 , all the way down to 5 degrees, and this allowed her, with the A833 and 3.55s to idle down to 550rpm in first gear and pulling herself along.
This is just one example of many that I have tuned.

Another thing IDK,
is how hard you have already tried to get this beast running. So it may be that I'm not telling you anything that you don't already know. In which case, I'm sorry to have wasted your time.

Edit
I forgot about these;
I once tuned a big Mopar Crate-hemi 4bbl and
a really stinky, really big-cammed solid-lifter 440 too .
I forget a lotta stuff these days.
So I was thinking
that if you have read this far, I could at least tell you a joke;
When I was a kid, my Momma told me that too much masturbating would make me go blind. Well by age 15, I was diagnosed with astigmatism, and Momma bought me my first pair of glasses.
Wait, I'm not finished yet.
So seven years ago my eyes began to get better and five years ago, I retired the glasses. There's been no change in my habits.
Wait, still not done.
Now almost 70, my wife of 46 years, tells me too much self-pleasuring will cause me to lose my hearing.
What?
Getting old is killing me, lol.