First of all, it is not my intention to turn this into a "points vs. electronic" discussion, especially since the O/P is a new member. That being said, I would like to make some comments on post #5. First of all there are thousands of flatheads out there running mechanical advance only distributors on the street with no problems. The only problem with them is that they may not deliver optimum fuel economy. I am running two myself, one on my '51 Ford and one on my "Hot Rod" engine. I use the '51 as my summer daily driver and it performs flawlessly. It delivers 14 MPG around town and 19 MPG on the highway with no OD.
Secondly, the method that a distributor uses to advance the spark has absolutely nothing to do with the amount of total advance. Flatheads like a total advance in the low 20 degrees neighborhood, and whether that is done solely by vacuum (as in a stock Load-a-Matic) or mechanical only, or a combination of the two is irrelevant. The main problem is that most aftermarket distributors for flatheads come with a built in advance curve more suited to an overhead valve engine than a flathead. Most have a maximum of about 36 degrees, which is fine for a SBC but way too much for the average flathead. If the present distributor was converted by someone who knew what they were doing (and most do), it will have the total advance limited to the proper amount, and if in good shape, should be a perfect fit for the engine.
I realize that it may be tempting to throw the latest gizmo at a problem and hope that it fixes it, but that way is usually counter-productive and often expensive, I checked and see that the MSD unit mentioned above is north of $600! I had an MSD distributor in a 276 Merc in a '36 coupe I had 25 years ago, and while it produced a good hot spark, the engine always had an overheating problem. It turned out that the distributor had the dreaded "Chevrolet curve" and the engine was running way advanced.
As another poster has already mentioned, this sounds more like an over-rich carburetion problem rather than an ignition problem. I would start addressing this problem by checking the fuel system. I would check that the fuel pump is putting out the proper pressure (2 1/2 to 3 psi) and no more; this is one case where more is not better, as too high fuel pressure will overwhelm the needle valve in the carburetor and produce an over-rich condition. If the fuel pressure is proper, I would then turn my attention to the carburetor. Is it dirty? Has it got the proper jets? Does the power valve leak? Any one of these conditions can cause the problems you are experiencing. If you feel you are not up to tackling the carburetor yourself, there is a member on this forum ("Charlie ny") who is an absolute whiz at these things and can make your carburetor perform better than new. And I'll bet it will cost about half what the fancy MSD unit will set you back, and solve your problem. I am making the assumption that the O/P's vehicle has a stock carburetor.
I also find the last line in the post recommending an MSD distributor to be quite curious.