We present a stochastic geometry-based model to investigate alternative medium access choices for LoRaWAN---a widely adopted low-power wide-area networking (LPWAN) technology for the Internet-of-things (IoT). LoRaWAN adoption is driven by its simplified network architecture, air interface, and medium access. The physical layer, known as LoRa, provides quasi-orthogonal virtual channels through spreading factors (SFs) and time-power capture gains. However, the adopted pure ALOHA access mechanism suffers, in terms of scalability, under the same-channel same-SF transmissions from a large number of devices. In this paper, our objective is to explore access mechanisms beyond-ALOHA for LoRaWAN. Using recent results on time- and power-capture effects of LoRa, we develop a unified model for the comparative study of other choices, i.e., slotted ALOHA and carrier-sense multiple access (CSMA). The model includes the necessary design parameters of these access mechanisms, such as guard time and synchronization accuracy for slotted ALOHA, carrier sensing threshold for CSMA. It also accounts for the spatial interaction of devices in annular-shaped regions, characteristic of LoRa, for CSMA. The performance derived from the model in terms of coverage probability, channel throughput, and energy efficiency are validated using Monte-Carlo simulations. Our analysis shows that slotted ALOHA indeed has higher reliability than pure ALOHA but at the cost of lower energy efficiency for low device densities. Whereas, CSMA outperforms slotted ALOHA at smaller SFs in terms of reliability and energy efficiency, with its performance degrading to pure ALOHA at higher SFs.