Just continue with you beginner method for a while, I continued with it until I averaged under a minute.
These are the steps I took from the start.
1. I cubed for 1 week with beginners and got my times to around 55s avg.
2. Then I moved onto learning 4 Look Last Layer, and within a week (including learning) I got my averages down to around 50 seconds.
3. Over the next week I just kept practicing and got down to around 45 seconds average.
4. I then spent the next week learning intuative f2l and got my times down to around 50 seconds (higher than before I know).
5. Then for the next month and a half I've mainly been practicing f2l and just solving in general and now average around 35 seconds.
I'd advise you to go through a similar process, don't worry about the time alotments for each part, just the actual steps.
My next plan, after my exams, is to learn the rest of PLL and perhaps some OLL/F2L cases and actually drill certain things to improve them more

.
I hope this helps in some way;
Thanks.