Does the beer box have to be Asahi, Saporo, or will a domestic brand work?

Let's talk a bit about butyl rubber (inner tube rubber) and oil.

Butyl

Butyl (IIR) rubber is a copolymer of isobutylene. It has exceptionally low gas and moisture permeability and outstanding resistance to heat aging, weather, ozone, chemical attack, flexing, abrasion and tearing. It has good resistance to phosphate ester based hydraulic fluids, and has excellent electrical insulation performance. Butyl is not recommended for use when in contact with petroleum oils and fluids. The temperature range is -55ƒ to 120ƒC (-67ƒ to +248ƒF).

This rubber has very high impermeability to gases and is hence used for the inner tubes of pneumatic tyres, and in vacuum and high pressure applications. It has an unusually broad loss peak so that, despite having a glass transition temperature as low as -65C, it displays high damping at ambient temperatures It has good ozone, weathering, heat, and chemical resistance. Not suitable for use in contact with mineral oils.

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So, in hindsight butyl inner tube material might not be the best type of rubber to use for a gasket material.

And for those who say all types of rubber won't work, that oil will automatically attack all rubber types and turn it into goo -- what is that black ring like thingie that seals off every spin on oil filter made out of again?

Take a clue from the oil filter rubber gasket -- rubber works well with a very minimal pressure and your main sin that can cause a leak is to over-tighten (over crush) it.