After a bit of work, predicting OLL after first face becomes really easy, you can even get to the point where you try to cancel moves from your first face into the OLL, then after that, there are only 5 simple PBL algs (probably more like 20 if you want to do it rotationless). I’m to the point with Ortega where I can predict the OLL when the first side is 4 moves or less. This method would just be counting the first side and OLL as one step. Putting each piece oriented on its correct face would be a lot of algs, you would just be better off using Ortega.Isn't OBL essentially the same as someone who can predict OLL while using Ortega for the first layer? (Although learning the algs would obviously be more efficient, I am not sure if the cost of learning the specific algs would be worth it). However I am not a great, or even good, 2x2 solver, so take that opinion with a grain of salt.
OR: is your OBL simply properly orienting both layers without placing them into their correct layer? I.E, all white and yellow pieces facing up or down, but then can be on either layer.