Input for 340 upgrades

IMHO
for your dreams, you need either a bigger engine, or to take 400 pounds out of the car, or to supercharge it.
It is really hard to marry your requirements with just 340 cubes and 3300 pounds ready to race. I think it could be done with turbo(s).
However, it is possible to make a sweet streeter with what you have, and let the ET be what it will be. A mid twelve second car, is a very fun streeter.

What I would do:
Before I would use open chamber Eddies, I would pull the pop-ups and mill them to zero-deck plus .007, to use their closed-chamber heads, and the FelPro .039 gaskets.
I would ditch that cam for a fast-rate solid-FT cam.
I would wire that GVod to split gears, and I would, install whatever gears got me 88 to 90mph at shift rpm with whatever cam I chose, in SECOND overdrive.
And that 3500TC would be history.

Here is how, for a gangbusters streeter, I see this:
The .007 pop-up will give you a Quench of about .032. The new Scr will come in at around 10.4 with 5cc allowed for eyebrows.
The above combo at your elevation of 20ft? will like an ICA of 60 to 62 degrees, making pressure of at least 175/180 psi, and have so much bottom-end torque, that you will no longer need that 3500TC; say Goodbye to it.
As to the gears. Your 727 has ratios of 2.45-1.45-1.00.. Splitting will get you 1.91-1.13-1.00. Combining them you get
2.45-1.91-1.45-1.13-1.00-.78od At WOT, here is how you will use it;
2.45-1.91-1.45-1.13-.78od, skipping 1.00.. your splits are
.78-.76-.78-.69
You will gear it to hit about 88/90mph at shift rpm, in second over. If you have 28" tires, this will take 4.30s for 88=5670@10% slip. I chose 88 because At 3300 pounds this only takes 350 hp. Meaning street-friendly cam.
So your starter gear will be 2.45 x4.30=10.54, compared to 9.58 currently, which is plus 10%. Allowing you to drop 10% torque in the TC, to break even.
But your splits are now averaging 78% compared to 59% on the 1-2 before. And you are now gonna use 4 ratios to 88, instead of just two; so your average HP for the run will go up, so you can run less specific HP, for the same ET.
Furthermore, you can now run a 4-speed tight LSA cam, instead of a 112/114 auto cam.
So things are fast turning your 12 second car into a tame streeter.

I'm figuring this out on the fly here, so bear with me.
I see this working so well, that I'm gonna upcam one size to an Ica of 64*. This will give up some bottom-end, but your new starter gear of 10.54 can afford it. So now we are looking for 90 mph in the Eighth, which is ~465hp@3300 pounds; and the new rpm still with 4.30s, is....5800, I like it.
Going thru the traps at 5800 means you can have a powerpeak down around 5500. And that usually points to a 240* cam.
But I'm gonna guess;
that these 4 gear ratios over 2, are worth 1 cam size,and
the tighter LSA I want to run, is worth 1, and
the alloy heads are gonna add a couple of hundred to the top.
so; all-in-all,
I'll guess that you can down-cam at the very least, one size, so I'll guess a 232 cam @.050. Just FYI; I have a 367/A833/3.55s, and use a 230*FTH cam to hit 93mph at 3467 pounds. So I'm fairly confident this is working out as expected.
To make it streetable, to use a decent TC, I would choose a tight lash solid lifter cam, to net 232ish @.050 after lashing. And I would try a 106LSA.
So I'm shopping for a 270/276/110 after lashing.

Speaking of streetable;
with 4.30s x.78 your hiway gear is 3.35 and with 28s, 65=2600@zeo slip; could be 100 more depending on terrain. So there yago; I choose a 2600TC. That 232SFT cam will have a boatload of extraction degrees, with a minimal amount of overlap, so is a great choice to cruise with. I ran an HFT cam of 270/276/110 with .050s of 223/230; GREAT street cam.
The above is what I would do.
Is this the best recipe?
IDK, I'm not you.
I biased it to get some decent fuel mileage, and sacrificed quarter mile ET, cuz, IMO, for me, 10s is not realistic with a street 340.

Make no mistake; this is not a recipe to get into the 10s.
But it might do 90mph, in the Eighth, which in street trim is a sub 8 second ride, even spinning most of the way. You will need a rev-limiter. But I'm only targeting 350/360 hp, which is a cheap/easy target for a 340. You probably have that now with the 284/484 cam and iron heads.

Now, in street mode, you put the GVod back into automatic mode, and drive it as a 3+1. There is ZERO benefits to splitting gears in town, ZERO........ but you are now running 4.30s,lol, which is a stinking blast!

As you know, engaging overdrive, using the computer, it shifts soft and slow. And it is impossible to engage in reverse nor at slow speeds. The computer is protecting the unit.
To run the GVod, as a splitter, you have to bypass the factory computer, and put the unit on a toggle-switch ( I used a push-on/ push-off and wired up some colored LEDS, red/green, to tell me which way it was). Once the pressure is up,the unit will hesitate a few microseconds, and then POW!, it will shift like lightning;the higher the pressure, the harder and faster the shift. And if you do it with the tires spinning, they will keep right on spinning. With 4.30s, you can engage overdrive almost right away as soon as the car has moved maybe two car lengths; I'm guessing.

There are two caveats;
1) the GVod unit will not tolerate being engaged in reverse.
You have to figure out how to prevent this. Just one revolution in reverse cost me a rebuild plus shipping, plus border-crossing = a lotta lotta money. This is imperative. and
2) IIRC, the GV people told me that the unit will not out-shift properly under load. I was running a clutch, so no problem for me. You, with a 727, will need to discuss this with your salesman.
Or perhaps someone will chime in.

Having said all that;
You might try the 4.30s and gearsplitting first, for a couple of weeks, until you get the hang of gearsplitting,; with no changes to your current engine at all; to see if I'm blowing steam. Try not to pizz your pants. And before you return home, wipe that silly smile off your face, cuzz the wify is not gonna interpret it the same way you do,lol.
Oh and make sure there is no loose junk to fly around your interior or trunk, cuz if it ain't screwed down, it will get airborne.

If it was me, I would run 4.10s and hope at 3300pounds your rig will be a lil faster than mine was. And I would try for a lil more than 10.4Scr. Some FABO members say they are running Qs closer to .020 than to .030, but that will only get you a part of a CC. But you might get away with less eyebrows, or, best idea; you might consider shaving your brand new ( 63ccs if I remember right) Edelbrock heads. I have run 185psi no problem in my 367, and on 87E10 no less. Some FABO members have stated to be running 200psi still on pumpgas.

BTW: definitions:
SFT is a Solid Flat Tappet cam, and
HFT is a hydraulic.
Scr is Static compression ratio
LSA is Lobe Separation Angle
Ica is Intake closing angle
TM is torque Multiplication