Learn English – grammar of “keep your seat belt fastened while seated”

You are right.

I had my hair cut = “I caused my hair to be cut”

In this causative construction cut is a past/passive participle and hair is its Patient, the entity acted upon. Compare the use of a verb whose past/passive participle is distinguishable from its infinitive:

I had my speech recorded^PaPpl = “I caused my speech to be recorded”, not
^∗ I had my speech record^Inf.

Note that if the HAVE NP VERB construction is employed with VERB in the infinitive, it does have an active sense; NP is taken to be the Agent of VERB, the entity which performs the action, and if VERB is transitive another NP acting as Patient/Direct Object is required:

^∗ I had Mario^Agent bring.
^okI had Mario^Agent bring my notes^Patient.

This may be ‘passivized’ by employing the participle:

I had my notes brought by Mario, which is the same construction as
I had my hair cut [by the stylist].

^∗ _{marks an utterance as ungrammatical}

You are overthinking the passive voice and objects of a transitive verb. To work and to travel could be used both as a transitive and intransitive verb. The characteristics of this kind of verb is it is very flexible in terms of having a direct object or prepositional phrase as its complement. For example,

He worked for nine hours. vs He worked nine hours.

For nine hours is a prepositional phrase and nine hours could be an adverbial noun. But the question is "why can't nine hours be an object of the verb to work?" They obviously can. Otherwise, you can't passivize the sentence.

Distance (which is/was) traveled by light

Hours (which were/are) worked by employees

All the above examples have so called "whiz deletion (omission of a relative pronoun + the verb to be)" and they are idiomatic expressions. If you contrast,

Distance for which light travels (traveled)

Hours for which employees work (worked)

You could notice that the former phrases are more concise.

Nobody writes "working hours" as "hours that workers spend for working". Why? Because the two words working hours are enough to express the longer phrase.

If you replace to work with to spend, it would be easier to understand.

He spent nine hours. vs Nine hours were (or was) spent.

"Hours spent by employees" would not be concrete enough compared with "Hours worked by employees" because to spend has a broader meaning than to work.

English is a flexible language. You should not care so much about this kind of structure as there is no hard-and-fast rule in terms of passivizing a sentence. There is just a general rule.

This room can sleep six guests.

This means six guests can sleep in the room. Can you passivize this sentence to:

?Six guests can be slept by this room.

A native speaker would say, "what?" Not all the transitive verbs could be passivized. In addition, an object that looks like an adverbial noun could be passivized. Why? It could be considered as an object of a transitive verb.