Your objection interests me, because these are both cases that I figured out myself with much contemplation and was quite content with many years ago and have never subsequently looked up in any reference (and I doubt your alternatives ever occurred to me). But after a spot of investigation now, I don’t believe you’re right on either count and stick to what I have written, at least for now.

https://duckduckgo.com/?q=let+tennis+hinder: the consensus among the first few results, which are reputable-looking sources, seems to be that the hinder sense is probably correct, though some suggest as an alternative the French filet meaning net.

https://duckduckgo.com/?q=etymology+of+let+and+hindrance: not much obviously canonical, but https://www.phrases.org.uk/meanings/without-let-or-hindrance... at least sounds reasonable, and agrees with me, including a citation in the last paragraph from 1799 which is unequivocally being used in the sense I nominated.