I don't have any experience with the SSVIII, I own an X-Cube. 3x3 stage will be harder on 4x4 just because there are more layers to move. Parity also slows down 3x3 phase. The best things to practice for decreasing your 3x3 phase of reduction is to just solve your 4x4 as a 3x3. Do an Ao50 or something. Also drill parity and LL algs.
Edit: Another thing that will add a lot of time is transition from reduction to cross. Don't spend 5 seconds looking for cross pieces after edge pairing.
Edit 2: I just did a quick Ao5 on my 4x4 and got 23.6 seconds. My 3x3 Ao50 I just finished was 21.1. There shouldn't be a 10-15 second difference at all. I'd work on transitions first and foremost. I did the 4x4 average with inspection btw