One word - Weldwood
Weldwood contact cement is your friend. Trust me on this.
Premium quality, brush grade, neoprene-based contact cement that meets the stringent requirements of the professional user. High strength and initial grab make it ideal for most projects. Fast-drying formula dries in 15-20 minutes. Offers high heat and water resistance when dry.
Please note that this stuff is extremely noxious and flammable, so use in well-ventilated areas.
Available at the usual places.