Sounds like old-style chains wear faster than bushingless and don't take lub quite as readily.
I have a number of gearhub bikes and single speed bikes, and I use 5/6/7-speed bushed or bushingless chains and 1/8" bushed chains indiscriminately.
I have noticed no significant difference in wear or lube retention between the different chains. Single-speed primary drive is very tolerant of pitch wear anyway, so I would just use whichever chain fits the sprockets best and costs least.
Have a good look at the stumpy, crude teeth on an ACS freewheel, which is one of the most popular brands of single-speed freewheel, and you will see how forgiving a single-speed chain drive can be.
