And those that didn't believe this, did they agree with each other on the human authorship of the Vedas? Or did they have any differences among themselves?
As you have stated in question, no need to provide answer for Mimansa (Pura Mimansa by Jaimini and Uttara Mimansa by Vyasa) which obviously declares Vedas Apaurusheya.
Now, regarding other schools, Yes, Samkhya and Yoga also believes Vedas to be Apaurusheya. Rickross's answer already cited how those school accepted Vedas as valid proof (Shabda Pramana).
According to Samkhya Sutras of Kapila,
Quoting Sanskrit text from Wikisource:
न नित्यत्वं वेदानां कार्यत्वश्रुतेः । सांख्यसूत्र-५.४५ । (वेदस्य नित्यत्वापौरूषेयत्वयोर्निरासः)
न पौरुषेयत्वं तत्कर्तुः पुरुषस्याभावात् । सांख्यसूत्र-५.४६ । (वेदस्य नित्यत्वापौरूषेयत्वयोर्निरासः)
मुक्तामुक्तयोरयोग्यत्वात् । सांख्यसूत्र-५.४७ । (वेदस्य नित्यत्वापौरूषेयत्वयोर्निरासः)
नापौरुषेयत्वान्नित्यत्वमङ्कुरादिवत् । सांख्यसूत्र-५.४८ । (वेदस्य नित्यत्वापौरूषेयत्वयोर्निरासः)
तेषामपि तद्योगे दृष्टबाधादिप्रसक्तिः । सांख्यसूत्र-५.४९ । (वेदस्य नित्यत्वापौरूषेयत्वयोर्निरासः)
यस्मिन् अदृष्टे ऽपि कृतबुद्धिरुपजायते तत्पौरुषेयं । सांख्यसूत्र-५.५० । (वेदस्य नित्यत्वापौरूषेयत्वयोर्निरासः)
Quoting English translation from The Sankhya Sutras of Kapila Translated by James R. Ballantyne:
Aph. 45. * The Vedas are not from eternity; for there is Scripture for their being a production.
a. Then are the Vedas the work of [the Supreme] Man? To this he replies, 'No':
The Lord not the author.
Aph. 46. * They [the Vedas,] are not the work of [the Supreme] Man; because there is no such thing as the [Supreme] Man, [whom you allude to as being, possibly,] their maker.
a. Supply, 'because we deny that, there is a Lord.' 1 [This is] simple.
b. Adverting to the anticipation that there may be some other author, he says:
Who are not authors of the Vedas.
Aph. 47. * Since the liberated is unsuited [to the work, by his indifference], and the unliberated is so, [by his want of power] neither of these can be author of the Vedas]. 4
a. But then, in that case, since they are not the work of [the Supreme] Man, it follows that they are eternal. To this he replies:
Aph. 48. * As in the case of sprouts, &c., their eternity does not follow from their not being the work of [any Supreme] Man.
a. [This is] plain.
b. But then, since sprouts, &c., also, just like jars, &c., are productions, we must infer that they are the work of [the Supreme] Man. To this he replies:
Plants denied to be works.
Aph. 49. * Were this the case with these, also, [i.e., if it were the case that vegetables were works], we should find a contradiction to experience, &c.
a. It is seen, in the world, as an invariable fact, 3 that whatever is the work of Man is produced by a body. This would be debarred, &c., were the case as you contend; [for we see no embodied Supreme Man to whose handiwork the sprouts of the earth can be referred]. Such is the meaning.
b. But then, since they were uttered by the Primal p. 350 Man, the Vedas, moreover, are, really, the work of [the Supreme] Man. To this he replies:
Only what is voluntary is a work.
Aph. 50. * That [only] is Man's work, in respect of which, even be it something invisible, an effort of understanding takes place. 2
a. As in the case of what is visible, so, too, in the case of what is invisible, in respect of what thing there takes place 'an effort of understanding,' i.e., a consciousness that Thought preceded, 3 that thing alone is spoken of as Man's work: such is the meaning. Thus it has been remarked p. 351 that a thing is not Man's work merely through its having been uttered by Man; for no one speaks of the respiration during profound sleep as being Man's work, [or voluntary act]. But what need to speak of antecedence of Understanding? The Vedas, just like an expiration, proceed, of themselves, from the Self-existent, through the force of fate, wholly unpreceded by thought. Therefore, they are not [a Supreme] Man's work.2
And Yoga school is basically based on the tents of Samkhya and hence also accept that Vedas are Apaurusheya and Shabda Pramana. (adding sources as asked by OP in his comment)
One of the most popular commentary on Yoga Sutra is Vartika on Vijnanabhikhsu in which he many-times discussed that the principle is of Sankhya:
The same two Pramas of Samkhya are discussed in Yoga. - Yoga Vartika 1.7
Same 24 entities of Samkhya are presented in Yoga. - Yoga Vartika 2.9
The Karya-Karana (cause-effect) theory discussed in Yoga comes from Sankhya. - Yoga Vartika 3.13
Who experience grief and joy: Those are intellect and Purusha; which is endorsement of Sankhya.- Yoga Vartika 3.35
The Dharma-Dharmi (quality and attributes) relationship are also similar in both Darshana. - Yoga Vartika 4.12
The creation theory of universe from Akasha is also based on Sankhya - Yoga Vartika 4.14
Source of above quotations: योग_दर्शन. Though I've not quoted English translation for every quote, you can read it from Internet Archive as I discussed here. For justification, quoting one instance from page 61 for Yoga Vartika 1.1.4:
अत एव पुरुषार्थवत्येव बुद्धि: पुरुषस्य विषय इति सांख्यसिद्धान्त: - Yoga Vritti 1.1.4
Therefore alone (it is said) only that intellect which has the goal, is the object of the Purusha. And this is established theory of Sankhya that...
Brahma Sutra, after refuting the philosophy of Sankhya said that "एतेन योगः प्रत्युक्तः " means "By this Yoga philosophy is also refuted" - Brahma Sutra 2.1.3. So, it is obvious and clear that Yoga is based on most of the tents of Sankhya.