Thanks for all the great advice and suggestions. I stopped at the local Woodcraft store and was advised to use a product called Mineral Spirits first with a clean cloth and if it didn't work then do it again except apply with a light rub of 0000 steel wool. Turned out that it did need thw steel wool and it all came out without too much effort. The spots are now shiny aside of the dull veneer but that will change with an application of boiled linseed oil and then a good coat of wax.
Good to hear the foam residue cleaned up well for you.
Reading between the lines, here, but you mentioned that the finish that was under the packing inserts is shiny and the rest is dull. That leads me to believe that the finish has been altered by aging and the bits under the foam have been preserved (so to speak) by being covered. This would infer that it is probably a laquer finish. I actually owned the same speakers but can't recall what finish they had. Laquer was used extensively for speaker cabinets.
My concern is that you are going to apply Linseed oil and that may not be the best course of refinishing. Applying oil over laquer can be tricky, oil finishes are penetrating finishes and if applied on a non-porous surface tend to wrinkle and stretch, leaving the final surface sometimes rough. I think your Sansui's would be better served by using a different product for bringing back the lustre of the original finish.
The following is one way of refinishing lacquer finishes: First, clean the surface with a solution of TSP and water. This will remove soil and remove a lot of oxidation. Second, use a solvent such as mineral spoirits or lacquer thinner, lightly, with a rag, to remove any additional residue. Third, lightly sand, either with 400 or greater, wet and dry sandpaper or the newer abrasive pads. Apply new finish using either a brushing lacquer or spray. I think you will find that a spray lacquer works well on the ornate grills that are on these speakers.
If the above sounds too daunting, you could always try applying just wax in an inconspicuous area to see if it does the job. Sometimes that is all that is needed.
Good luck on refinishing your speakers.