We revisit the problem of entanglement-assisted covert communication over bosonic channels and show that the benefits of entanglement can be achieved with fewer entanglement resources than previously identified. Specifically, we show that $\calO(\sqrt{n}\log n)$ covert and reliable bits can be exchanged using $\omega(\sqrt{n})\cap o(n)$ Two-Mode Squeezed-Vacuum (TMSV) pairs and $\omega(1)\cap o(\sqrt{n})$ secret-key bits. The conceptual approach behind the result is to combine 1) soft-covering and secret-key resources as a coordination mechanism and 2) superposition coding in the form of a two-layer On-Off Keying (OOK) and Phase Shift Keying (PSK) to index channel uses in which TMSV pairs are encoded. This approach is related to the idea of quantum trade-off coding, specialized and extended to the covert communication setting. Our technical contribution is to develop one-shot bounds then specialized to bosonic channels.