A bit of a long winded post. Guys I am having issues with my 4bbl carburetor that I installed last winter. I have a 272 that is 30 thou over and the late ford replacement heads so compression is on the lower end along with a stock cam. I put a 57 B type intake on the engine this last spring and have fought with it ever since. 
So the carburetor is a 390 cfm 4160 that was 2nd hand and I rebuilt it. The rebuild included new throttle shaft bushings to make sure it was good and tight.
I have put on the quick change vacuum housing and have tried every spring tension. I have changed the vacuum housing from the 390 cfm without the check ball to one from a 600 cfm carb with the check ball to see if it helps and tried all springs. I have tried all pump cams and even put on a 50cc housing and tried all the cams including the brown and yellow ones. I have tried squirters all the way from stock which is 24 I believe up to 40.
I have made sure the arm is set so it squirts as soon as you get movement as there is not any slack. I have verified the float levels and have even tried raising and lowering them above recommended settings. I checked vacuum advance and distributor advance and timing is at 10 degrees initial. Vacuum at idle is 19" at 3000' in park and 15-16 in gear, it is a FOM, idle speed is 650 out of gear and 500 in gear. During my trials I discovered my fuel pump was weak so I changed it and it starts perfectly now, but I still have an issue.
The issue is that when I do anything other than a creeping acceleration I get a bog that can stall the motor AFM shows lean and it always lets me know when the secondary's kick in when cruising and give it more gas. If I step on it it seems to go fine. Is there any ideas you guys have? I am wondering if the carburetor is too small and the secondary's are coming in too quick? I am at my wits end and want to figure this out over the winter.

Have you tried raising the float level? Also keep in mind that the secondary side of the carburetor has a ‘fixed’ idle circle and if it’s not working, then the primary side idle circuit will be running lean.  Something else to consider is warpage at the throttle plate to the main body.  How responsive are the idle mixture screws when setting the fuel mixture at idle?  If unresponsive or not very sensitive, then look for a leak at the aforementioned throttle plate to main body gasket or an internal problem with the carburetor circuits.  Don’t rule out the valve lash adjustments either.  Does not sound electrical but if a points distributor, make sure the grounds are good and that the condenser is tight within the distributor.

Lorena, Texas (South of Waco)