This paper describes the development of a platform to study astrophysically relevant nuclear reactions using inertial-confinement fusion implosions on the OMEGA and National Ignition Facility laser facilities, with a particular focus on optimizing the implosions to study charged-particle-producing reactions. Primary requirements on the platform are high yield, for high statistics in the fusion product measurements, combined with low areal density, to allow the charged fusion products to escape. This is optimally achieved with direct-drive exploding pusher implosions using thin-glass-shell capsules. Mitigation strategies to eliminate a possible target sheath potential which would accelerate the emitted ions are discussed. The potential impact of kinetic effects on the implosions is also considered. The platform is initially employed to study the complementary T(t,2n)α, T(3He,np)α and 3He(3He,2p)α reactions. Proof-of-principle results from the first experiments demonstrating the ability to accurately measure the energy and yields of charged particles are presented. Lessons learned from these experiments will be used in studies of other reactions. The goals are to explore thermonuclear reaction rates and fundamental nuclear physics in stellar-like plasma environments, and to push this new frontier of nuclear astrophysics into unique regimes not reachable through existing platforms, with thermal ion velocity distributions, plasma screening, and low reactant energies.