Nice motor.
What we've got here is the dreaded "tri-carb bog". The only solution is to yank the complete motor and ship it DIRECTLY to me!
But, short of that there are some cheap and easy fixes - and some fixes that'll cost a little of the green.
Which center carb and dist do you have?
1.) Free or cheap. This is CRITICAL. Convert the throttle linkage to a "progressive" linkage. That is so the center carb opens about 1/2 to 2/3 and then the end carbs start to open. Then all three hit Wide Open Throttle (WOT) at the same time.
In the picture, it looks like you have an Edelbrock or Offenhauser intake. It SHOULD have linkage that will do this by adjusting the slides on the rods. If the linkage is not the original Offy stuff, search for a picture of what it looks like, and duplicate it.
2.) Free or cheap. Test the distributor for vacuum advance. To test the advance, take the cap off, and then disconnect the vacuum hose at the carb. Suck on the carb end of the vacuum hose and watch if the advance plate inside the dist to see if it moves. If it does great!, if it does not - hmm, work to do.
Next take the vacuum hose off of the dist. vacuum can and put the other end back on the carb/manifold/where-ever it was, and start the engine. Does it suck? If not, have you got a mismatch of center carb and dist? Early dists used "ported" vacuum. If there's anything wrong with your distributor, jump to #5.
3.) Free or cheap. Get a 3 foot or so length of rubber tubing. Put one end in your ear and the other end to possible leak areas. With the engine idling listen around the carb bases and where the o-rings hold the aluminum carb to the cast iron manifold. Where-ever you hear a hissing you have a vacuum leak.
Also stick the tube down all three carb and compare the "hiss". The center carb should be much louder. The two ends should be mostly silent.
Even from this great distance, I am suspicious of the o-ring seals between the adapter and the cast log.
4.) Free or cheap. Check the timing. If you don't have a timing light, I'd strongly suggest buying yourself one for Christmas. I'd reccommend the type with the knob on the back to "Zero" out the timing.
You need at least 12 degrees initial advance (BTDC) set with the vacuum hose disconnected from the distributor and plugged with a golf tee. Don't forget to reconnect the vacuum hose when it is all set. Your engine will idle nicely wilth the advance so far off that the only thing it'll do when you step on the gas pedal, is die.
What Doug was telling you about the timing, was that you need to leave the timing light hooked up when you hook up the vacuum hose to see if the spark jumps WAY up. (You can use the knob to zero it, and read the total advance.) Then disconnect the hose again, and with the light still hooked up, rev the engine to see if the mechanical advance is working correctly. The advance should again increase as you increase the revs. (Again, you can use the knob to zero it, and read the total advance.)
I once had a v/8 Pontiac with 3 twos. It ran like crap with the stock distributor. Yup, the dreaded "tri-carb bog". An old fart showed me the solution. It was to leave the vacuum advance disconnected and recurve the inside the distributor's mechanical advance. Do a search on the forum and read the articles on recurving the DS II. (hmmm... now I'm the old fart)
5.) Some money. GET RID OF THE STOCK DISTRIBUTOR! If you like new high tech, get FSPP DUI electronic distributor. I'm told it works much better than the Ford DuraSpark II (DSII) electronic distributor. The DSII will be head, shoulders and stepladder better than your stock distributor, so the DUI is stellar.
The DSII can be got at virtually any junk yard - do get ALL of the wiring and associated parts with it. (Cap, plug wires, ign module, coil, wiring harness between the coil and the module and the dist.) You can also get a new/rebuilt at virtually any parts store. The DS II uses manifold vacuum. The DUI can be had at FSSP (ad at the bottom of each thread) You mention a Mallory Unilite w/o vacuum. That is a good solution too, but IIRC it still has points. IMHO, go electronic.
6. ) Go back to the first paragraph and just ship the whole works to me - actually it would be best if you just dropped off the whole car in my driveway and left the title on the dash and the keys in the switch.
PS welcome to the Ford SIX Forum.