You really cannot tell rich/lean by the sound of the miss.
When you put ANY carb on, the first thing you ensure is that it gets the idle speed screw preset so that the butterfly or throttle blade is exactly right at the edge of uncovering the transfer holes or slot, so that even five or ten thousandths of movement instantly begins to uncover the slot or holes. That is the correct dead on idle setting and better than one turn on the screw which if not checked means nothing. With the idle at that point then you have the full range of off idle fuel flow and instantly. If the car does not idle at proper speed then, you have to add airhole to fake motor into thinking blades open further than they are. Having carb preset like that before you bolt it down then helps much to determine what is happening when you roll throttle open, since you already have a known point to start with. If you don't know, then you do not know whether the resultant miss is before you hit transfer or during or even past all of it. In other words doing it definitely the hard way with much more confusion.
Just looked at a cutaway of the idle circuit on a regular 5200, it clearly shows that the mixture set screw sets idle fuel at the curb idle hole only and NOT the transfer slot. The transfer gets the full idle jet fuel, the curb hole lower gets the mixture set fuel, two things to keep sorted out there. If the mixture screw is only one turn out that may well mean too RICH off idle, the screw is in very far to cut way back meaning a LOT of fuel coming though idle jet. Get somebody to go back at tailpipe and look to see if any black smoke comes out when you slowly roll the throttle on to get into your rough running area. And of course that thinking only valid if you have the starting butterfly position as I just said. If you are into the transfer, then you may be too rich because of that, or lost. You're now adjusting mixture based on incorrect throttle blade position, or wrong.
Proper dead idle is with all idle fuel coming through the curb hole only and none through the transfers. But the transfers should then work instantly as soon as blade gets moved.
Why I use a fitting welded on exhaust somewhere to insert a narrow band O2 sensor, you can tell by the output which way to go. Screw all that guessing.
More. Just where is the idle speed setting for the OTHER barrel? If it even has one. There is usually another idle circuit in the other barrel. If 1/1 ratio and both open together, you may have complicating issues from that side too. The mixture may not be settable there, but the position of the butterfly there could be adding to the problem. Most people never even think about that one. Generally the other barrel sets just like the front, or right at any slight movement the transfer exposes, but just barely covered up at dead idle. The aircrack around the throttle plate then usually will work fine with the 'front' barrel, or the one with the mixture screw. Lots of time the other will be almost shut, which makes you have to open the one causing you trouble more, or the source of your trouble to begin with. Like on a 4 barrel, you want balance, throttle blades almost closed have to open a bit before fuel flows and troubles there. All 4 need to be cracked open a bit already, it establishes initial slight flow so that it does not have to be started up, making off idle smoother. Fuel circuits already in motion can react quicker to changes.
Try getting the idle speed screw deeper to see if you can get the idle speed fast enough to get into your bad running spot. If so, then while it is there then screw your mixture screw SHUT and see if the bad running gets better or worse. That may give you an indicator of which way the idle jet needs to go. I've been known to take extremely small OD pieces of wire and stick them into the idle jet to cut the size of the hole back, I lock the piece of wire in a side airbleed hole to keep it in place. If you know the size of the wire and the size of the idle jet hole, then a little calculating of the two areas and subtract one from the other can tell you what new size jet you need.
Sorry to choke you there......... .........