Strong-coupling of monolayer metal dichalcogenide semiconductors with light offers encouraging prospects for realistic exciton devices at room temperature. However, the nature of this coupling depends extremely sensitively on the optical confinement and the orientation of electronic dipoles and fields. Here, we show how plasmon strong coupling can be achieved in compact robust easily-assembled gold nano-gap resonators at room temperature. We prove that strong coupling is impossible with monolayers due to the large exciton coherence size, but resolve clear anti-crossings for greater than 7 layer devices with Rabi splittings exceeding 135 meV. We show that such structures improve on prospects for nonlinear exciton functionalities by at least 10$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$, while retaining quantum efficiencies above 50%, and show evidence for superlinear light emission.