blackriverfish, I suggest you take advantage of a free download of the full service manual for your engine, which includes detailed carburetor overhaul information:

http://th.manualwebsite.com/pdf/4-cycle_ohv.pdf

Your carburetor is described as Series 3 or 4, so do not be distracted by instructions for the other types, up through Series 10 and the Walbro LMK used on the last of the OHV Tecumsehs.

Tecumseh carburetors have a fairly evil reputation, but most of them can be serviced very successfully by following the instructions and having a kit of service parts close to hand. Note the warning not to remove any "cup or ball plugs", but this does not apply to ordinary Welch plugs provided replacements are included in the overhaul kit. (However, I personally don't remove Welch plugs unless every other approach fails, which it seldom does.) I think you will need to use a spray can of proper carburetor cleaner to actually get the gum out, but do not put it on plastic or elastomer parts, and blow it out immediately after spraying it on or squirting it into passages. In my experience, lesser solvents do not remove hardened gum (and emulsifiers, in particular, often require multiple blasts to get the small radial holes clear. On Honda carburetors I often have to use jet drills on the radial holes of less than 0.5 mm).

Here is a diagram showing the working parts of your carburetor:
[Linked Image]

As I said previously, I currently suspect that there has been foul play in that carburetor, and you need to be on the lookout for "tenant's improvements" made before you got this machine. Look especially for signs that the "main nozzle" (a combined main jet and emulsion tube) is either fouled or modified. If you are lucky, it is badly fouled and the previous tenant amputated the working part of the main adjustment screw to compensate for this, rather than clean it out, then when the fouling progressed even further and it became lean despite the amputated adjuster, he/she disposed of the machine.

We are here to help at any time. Please don't become one of the people who conclude that Tecumseh carburetors are unfixable garbage: they are not unfixable unless made so by previous attempts to repair them.