I gave up on automotive grease, and any petroleum grease, long ago. It won't dissolve nearly as well in the hot, soapy water I use to clean my guns.
I've also found that with black powder -- which is about all I ever use -- petroleum greases create a hard, tarry fouling.
I use felt wads soaked in the lubricant I introduced years ago, and named after me: Gatofeo's No. 1 Lubricant.
The recipe is:
1 part canning paraffin
1 part mutton tallow
1/2 part beeswax
All measurements are by weight, not volume. Use the ingredients stated; any substitution results in an inferior lubricant.
This is basically the recipe that 19th century ammunition factories used for outside-lubricated bullets. My contribution was to list very specific ingredients, which work well together.
This lubricant is too hard for cold weather but it works wonders in a felt wad.
I rarely use grease over the ball, unless I've loaded so much powder in the chamber that there's no room for a greased real wool felt wad. I specify real wool because so much felt today is synthetic, made of plastic, and doesn't work as well. In fact, I've had polyester felt leave deposits of melted plastic in the bore.
I live in the remote Utah desert where temperatures can go as high as 110F (43.5C). When it's this hot, and humidity is almost nil, I may have to put grease over the ball to augment the greased felt wad. But usually, this is not required.
When I do use grease, I use CVA Grease Patch. It doesn't harden in cold weather and provides excellent lubrication.
Incidentally, Dixie Gun Works sells an all-brass lubricator for cap and ball sixguns. I bought one 20 years ago for $10 as I recall. Probably three times that today!
But it's machined from solid brass, the rear screws off for easy loading, and it had a threaded brass plug for the end, so it won't leak.
But your idea works well. And you can't beat the price!
For me, greased felt wads are easier, work better and are less messy.