I don't wish to open the Batwing vs dual inlet 4bbl air cleaner debate I just used Bat wing because it sounds cool and some still say that's what it is.
Anyway my 56 Olds Super 88 is mostly stock ( thats what I prefer) except for the following mods, 1. power frt disc brakes, 2.alt (vs gen)
3. a knee freezer A/C 4.addition of a Edelbrock performer 4bb carb and 5 last but not least Flowmaster dual exhaust. these mods were made by the prev owner and I'm ok with them its still bone stock in appearance down to the paint code, but that damn Edelbrock aftermarket air cleaner was driving me crazy, I'm sure he did it because the air horn on the Edelbrock is a different diameter than the original oil bath air cleaner, (the Edelbrock runs just fine idles and drives fine if it aint broke don't fix it)
The alternative was the aftermarket repo for $159 or more or modify the existing oil bath which the prev owner provided. no brainer I got lucky the base of the Edelbrock was the same external diameter as the original, so all I had to do was gut the orig air cleaner and find the proper dry paper element which was a WIX 42088 (some one here on the forum provided that # ) it was very close just about 1/4 inch to short however a $3.88 roll of foam door weather strip around the top of the filter solved that,
next was paint,I removed all the old paint with a mixture of carb cleaner, brake clean and a wire brush (pain in the ****) I didn't want shiny penny new look I wanted kind of the survivor/semi restored look so I went with satin paint and a light rub after drying with very fine steel wool to achieve the patina look .
so combining the two air cleaners worked it's a hybrid !! here's a few pics before and after.I like the factory unit !!

 

Looks great. I have a paper filter on my 54. Now all you need to do is get the little decal from Fusick that goes on the front of the batwing.