We report magnetotransport measurements on the quasi-two-dimensional charge-transfer salts Љ-͑BEDT-TTF͒ 4 ͓͑H 3 O͒M͑C 2 O 4 ͒ 3 ͔Y, with Y =C 6 H 5 NO 2 and C 6 H 5 CN using magnetic fields of up to 45 T and temperatures down to 0.5 K. A surprisingly robust superconducting state with an in-plane upper critical field B c2ʈ Ϸ 33 T, comparable to the highest critical field of any BEDT-TTF superconductor, and critical temperature T c Ϸ 7 K is observed when M = Ga and Y =C 6 H 5 NO 2 . The presence of magnetic M ions reduces the in-plane upper critical field to Ϸ18 T for M = Cr and Y =C 6 H 5 NO 2 and M = Fe and Y =C 6 H 5 CN. Prominent Shubnikov-de Haas oscillations are observed at low temperatures and high magnetic fields, showing that the superconducting salts possess Fermi surfaces with one or two small quasi-two-dimensional pockets, their total area comprising Շ6% of the room-temperature Brillouin zone; the quasiparticle effective masses were found to be enhanced when the ion M was magnetic ͑Fe or Cr͒. The low effective masses and quasiparticle densities, and the systematic variation of the properties of the Љ-͑BEDT-TTF͒ 4 ͓͑H 3 O͒M͑C 2 O 4 ͒ 3 ͔Y salts with unit-cell volume points to the possibility of a superconducting groundstate with a charge-fluctuation-mediated superconductivity mechanism such as that proposed by Merino and McKenzie ͓Phys. Rev. Lett. 87, 237002 ͑2001͔͒, rather than the spin-fluctuation mechanism appropriate for the -͑BEDT-TTF͒ 2 X salts.