Actually, the more strict way to interpret "sabhāvena suñña" would be "empty by way of own nature", not "empty of own nature", after all, the sabhāvena is an instrumental. Though the instrumental sense of "in terms of ..." is also not uncommon.
From something I wrote a year or two ago:
In his translation of the Pṭs, Ñāṇamoli (1982b: xvii, 362 n1) adds from Mahānāma’s commentary on the phrase “sabhāvena suññaṃ”, which he translates as “devoid of individual essence”, giving three possible renderings. 1. Empty of essence or arising of, or by, itself. This means that it has essence or arises, but this is due to other conditions, relating it to dependent origination. 2. Empty of essences other than itself, it has it’s own essence (sabhāva) but not other essence (parabhāva), as per “X is empty of non-X” (see below in Pṭk). 3. Empty as it has emptiness for it’s own essence. This brings in the abstraction of suññatā rather than just adjectival suñña, though also does tend to reify that abstraction as the very nature of dhammas. Ronkin (2005: 93f, 100) shows that Mahānāma’s oscillation between definitions shows his difficulty in reading commentarial tradition ideas of sabhāva into this earlier text, and the ambiguity in Pṭs in the first place. However, as Warder points out, it is really only Mahānāma’s third explanation which is convincing (cf. Ñāṇamoli 1982b: xviii).
The first explanation is the "empty of own nature", but it is the third that actual makes sense in the text, as Warder points out.
As Geoff says: "The Paṭisambhidāmagga wasn't composed at the Mahāvihāra." But, the Xuanzang stuff is far too late to make much influence on the issue here, probably about 800 years earlier.
"Which Hinayana texts teach the emptiness of all phenomena?"
"For example, the Satyasiddhiśāstra. If more Mahāsaṅghika texts had survived, we would likely have many more examples."
Yes, the Mahāsāṅghika had many groups that upheld this position. The status of the *Satyasiddhiśāstra is in dispute: Some Chinese took it as Mahāyāna, but it doesn't posit any Bodhisattva path, and the layout in four truths is straight out of the same book as the Sarvāstivādins, really. The author was originally a Sautrāntika, but later took up Mahāsāṅghika positions. So, it is halfway between these.
As Namdrol says, "it is not a representative of general Mahāsaṅghika", and the author probably had some Mahāyāna influence. Hard to attribute it to any specific school, but just see influences here and there. And I think that is the correct way to look at a number of systems around this time.
But, as I mentioned earlier, check out the so called Mahāsūtras (cf. Skillings). These are Sautrāntika sūtras that have some definition "all dharmas are empty" type teachings. They are not present in the Pali, and even some of them have been lost. Vasu quotes them a fair bit in the Kosa, too. And, check out the Mahāsaṅghika commentary to the Ekottarāgama in Chinese, as well. Also the Mahāsaṅghika school Lokānuvartana Sūtra 《佛說內藏百寶經》, which is heavy on the emptiness thing.