Just realized I haven’t read the original post thoroughly enough.
I think the second one (intransitive) should be 広がる. The “out” part might add to the meaning and there might be other words in Japanese which fit the bill a little better. I also kept 広げる as “spread out” for lack of a better synonym.
Jisho lists “erect” as one of the meanings of 立てる. Perhaps that also works? However, there is a different 建てる which is closer in meaning to “erect”.
I had the exact same problem… These two eluded me for a long while, because they’re challenging to translate into English. It helped me to look up other words using the 通 kanji .