I think you correctly identified very broad tendencies. However, as noted in the comments, there are many counterexamples to each one of your first four rules, so many that they shouldn't fall under rule 5 "exceptions".
- Compound kanji words are read as on'yomi
There are many pure kun'yomi compounds
and compounds with mixed readings (called jūbako yomi or yutō yomi, see Can a Japanese word combine both on'yomi and kun'yomi characters?).
- Single kanji words are read as kun'yomi
Again, not always.
- Verbs composed kanji followed by okurigana are read as kun'yomi
There is a broad class of verbs derived from so-called "suru verbs", which take an on'yomi kanji and some form of suru that has changed through sound change
However, this class is easily identified, so you may also put it under the "exceptions" rule.
- Geographical and personal names are read as nanori
Not every name is a nanori reading (unless you say that nanori readings include all standard readings, in which case this isn't really a rule at all).
小林 愛子、林 愛、黒川 慎太郎
(Then, the only rule I can think of for reading names is "anything goes". Also see Both on'yomi and kun'yomi in a first name?)
Rule 5, however, is a good rule.
- Exceptions to the above that need to be memorized
There will always be exceptions that need to be memorized.