質問: After some research on my own (looking through the list of kun-readings for more obscure kanji), I can more or less surely claim: に is 于 (which is simultaneously many things, including ここに and を); まで is 迄; の, of course, is 之. But what for the others? Are there specific kanji for は, for が, for で etc.?
回答: At one time, kanji used to be used to represent Japanese particles, but that is no longer the case for the most part (in Modern Japanese). Particles existed in Japanese long before there was a writing system. Kanji were borrowed from Chinese but since there was no equivalent to post-positional particles in Chinese, there were no kanji which could be assigned to particles. In those days scholars attempted to represent particles by using kanji phonetically (ignoring the character's meaning). For example, the particle には was once written as 庭 because the word it represents in Japanese is pronounced 'niwa'. However, ultimately this method proved unsuccessful, probably because it was excessively complicated or confusing. It was only with the evolution of the kana syllabaries that a standardized model of representing particles in writing began to take root. Incidentally, Katakana was originally used as 'furigana' in old kanbun texts as pronunciation markers. The priests would do things like writing an ヲ above or between kanji words to indicate to the reader that a particle should be inserted there. It is possible that these older methods of representing particles could theoretically still be used to write Japanese particles. As you mentioned you could say that に can be written as 于. So while I wouldn't call it 'incorrect', it wouldn't be natural to do so. These representations are quickly dying out and it is overwhelmingly the case that standard Modern Japanese favors Hiragana in writing particles.