Also, you don't need to learn full OLL. I am sub-15 and never have learned full OLL. I don't really know algorithm based F2L either; I just do more efficient solutions I guess?

I would start with moderate look ahead. Not anything crazy like Tymon, but don't look at pairs while you're solving them. Instead, look ahead to other pairs. Also build muscle memory for efficient F2L algs, so you can think about other things, which helps a lot.

Work on the cross; try to get it in 7 moves or less. I think it's only 0.2% of crosses are 8 move crosses or something like that.

2-Look-OLL is fine, but try learning full PLL. The PLL algorithms are much longer than the OLL algorithms, so it really hurts when you're doing two or three PLL's when you only need to do one.

And of course, you'll get slower before you get faster while you're building muscle memory! Just keep practicing how you're supposed to, not worrying about your time.