We study low-overhead uplink multi-access algorithms for massive Internet-of-Things (IoT) that can exploit the MIMO performance gain. Although MIMO improves system capacity, it usually requires high overhead due to Channel State Information (CSI) feedback, which is unsuitable for IoT. Recently, a Pseudo-Random Beam-Forming (PRBF) scheme was proposed to exploit the MIMO performance gain for uplink IoT access with uniform channel and load, without collecting CSI at the BS. For non-uniform channel and load, new adaptive beamselection and random-access algorithms are needed to efficiently utilize the system capacity with low overhead. Most existing algorithms for a related multi-channel scheduling problem require each node to at least know some information of the queue length of all contending nodes. In contrast, we propose a new Low-overhead Multi-Channel Joint Channel-Assignment and Random-Access (L-MC-JCARA) algorithm that reduces the overhead to be independent of the number of interfering nodes. A key noveltyis to let the BS estimate the total backlog in each contention group by only observing the random-access events, so that no queue-length feedback is needed from IoT devices. We prove that L-MC-JCARA can achieve at least '0.24'' of the capacity region of the optimal centralized scheduler for the corresponding multi-channel system.