My "avatar" TA-22 with a mild 2T has the OEM oil pump.
For my last couple of runs at Wakefield Park I ran an oil cooler form an adaptor plate. The OEM pump could not pump enough to match the "non oil cooler set up" pressure.
My oil cooler core may have been the restricting limit as pressure came up a bit more when hot.
Anyway my biggest problem was oil surge in the sump. The motor ran dry the last time out and rattled the bottom end. I was hoping the extra capacity created by the lines and cooler would help to absorb some of the surge, but to no avail.
My Competition 2T uses the TRD Oil pump made for the 2T/2T-G and has baffling in the sump. This combination gives me good oil pressure through the cooler.
t_temperley
You may find that putting baffling into the sump and running the OEM lower capacity pump will work fine.
As far as I know 2T, 2T-G and 3T motors run the same oil pump. If the 3T-GTE pump is bigger (ie has a thicker set of gears and a spacer plate) then it should be compatable to the other "T" motors.