I'm not so sanguine about the MLB, either. Yes. The state of the battery gives one the cold horrors, to be sure an' all, but the cage generally and its connection to the MLB will need some rigorous work and checking. The case of the crystal, being probably nickel-plated, has patently not appreciated the alkaline effusion from the battery.

The 'no goo' part of your parting statement may be worth reassessment. The third and fourth MLB shots appear to show your use of a flash to take the pics. Is this so? Notice that the reflectivity of the lacquer differs, being much less in the fourth pic than in the third. Add the apparent brown stain in the same area in the fourth pic, and the total is definitely the need for a good wash, whether you use the dishwasher, a fire-hose or the spraybottle that I recommend. That is the preamble to recommending a complete recap with tantalum electrolytics as well as the wash. Whether or not it is so that there is goo on the bulk of the MLB, you are lucky that the large axial caps under the PSU have not alsp puked onto the board. There are not that many of the SM aluminium electrolytics, so replacement is an assurance of continued functionality when you get the PSU tamed.

Whether the associated caps of the audio circuit have visibly failed or not, you should also be able to rescue sound out as a result of the recap.

Best of fortune to you in the endeavour.

de