If you have already started your TPS EAD then i think your status would go as TPS EAD ad far as I am concerned. But if you have not used your TPS EAD then I would say apply for OPT EAD and be in status as F1 and try working on OPT EAD. Keep your TPS status as backup plan. With your OPT EAD you will be able to work for a year depending on background of studies, in terms of STEM extended to 24 mths more. TPS just use it as backup. But I think i saw it in other posts as well saying you can apply for TPS EAD anytime even after registration period if you have TPS approved. But followup on that within other posts. I am not sure though