I think RIG would be great on your chamois.I do not know if it has any any lanolin in it,but it is a grease that has a similar texture/feel to it.
When I put a tool such as a chambering reamer away,I coat it with RIG.
RIG is not a new high tech product,I believe it has been around longer than I have...and I get Senior Discounts.
Another product I have(shop was out of RIG) is Break Free Collector.You might read the label on a bottle and see what you think.
My next old school idea,I do not quite recomend,as it would be really flammable.The old South Bend Lathe owner's manual recomends disolving petrolatum jelly(vaseline) in naptha and slopping it on machines to preserve them.I'd skip the naptha. Its as flammable as gasoline.If you want to experiment,vaseline would probably work good.
Stuff like Kroil if a good penetrant,but I think probably it is volatile...it will evaporate away after a while.