So I had the same problem when I bought my '84. Actually worse because the cups were pitted as well. I don't think the BB had ever been serviced considering the remaining grease was basically petrified. Anyhow, are your cups in good shape? If yes, you could always try the shorter spindle, but I think it might be too short.

I ended up buying a sealed bottom bracket with 127mm spindle from Velo Orange and it worked out great. No additional spacer (to make it asymmetrical) needed.

If you go from 5 to 6 speed, I think you'll definitely want to stick with the longer spindle length for better chainline. If your wheel is dished the same as mine, you should have enough room for the six speed freewheel without extra hassle.



Freewheel removing/replacing is fairly straight forward and the tools, although several varieties, are fairly inexpensive. Here's a good video on freewheel removal:
If your 1000 has the original wheelset, the hubs are sealed bearing Suntour and require harder to find specialty tools to fully service and/or replace the bearings. If the feel smooth, I would leave as is. If they feel grimy, it might be time to replace the bearings which might seem complicated depending on your skill/comfort level. There are a few threads here that cover this.

Suntour "sealed bearing" cartridge hubs
Sealed hub bearings: to replace or not to replace?
Suntour TA260 Hub Tool
Suntour cartridge bearing hub tool - any pictures?
Mystery Tool