As others have noted, the amount of alcohol to ensure death is uncertain and the methods of introducing lethal amounts vary person-by-person in such a manner that there's not a reliable way of saying.
Some may point to the first (or new) party-er that drinks so much they pass out on their back and die due to vomiting and aspirating said vomit
or know of a friend that drank so much they drowned in a small puddle/their vomit/insignificant thing
and then there's straight alcohol poisoning where they died from the CNS depressant alcohol introduces
the issue with all of them (and especially the last) is that the body is ready and able to survive a lot of those off-chances and risks to death through involuntary SI
As for the introduction of enough alcohol to die via rectal and/or intravaneous methods, it's uncertain. It's painful, and it's not quick.
You may find an article or statistic that supports your method, and by all means if that satisfies your doubts go for it.
I can tell you this website is pessimistic, but in a good way. There's a lot of vetting of methods and sources for the most reliable and least painful methods and those are the proven ones. The rest are usually outliers with little to no substantiation.
At the end of the day you have to ask yourself, what do you want more, a means to an end, a reliable means to an end, or a reliable, pain(less) means to an end? and choose and plan accordingly.