i got to under a minute when i began to 'learn' freidrich. i say 'learn', because my Friedrich is, and always has been, intuitive. you dont need to learn the algs.
not only is your spelling of Fridrich incorrect, it is inconsistently incorrect. although i agree that f2l should be intuitive
Learn Petrus. That does away with memorization, for the most part,
you shouldn't lie...
both fridrich and petrus have intuitive f2ls. and unless you can intuitively solve petrus LL, i think they both have memorization. and though you can claim that even though intuitive fridrich f2l still uses "algorithms" i am willing to bet that you subconsciously use "algorithms" for certain situations while blockbuilding.
And always start with the same colour. The system you use, requires a lot of moves and fast recognition is essential, and being color neutral doesn't save that much moves.
WRONG!!!! if you start practicing color neutrality now, it will be be very easy in the future. since you are still a beginner, it will be easy for you to learn to recognize cases for all colors later on if you start now. and color nuetrality is especially important if you learn petrus or roux. i know a color nuetral cuber that can get around 15 sec avgs, and he says that he doesnt even really realize the difference in colors.
I was averageing around 45 seconds with my own method before I changed to fridrich, which I think was a mistake, because Fridrich requires learning alot of algorithms, it's kinda repetetive and not nesseceraly that fast.
i do not know what your previous method was like, but if it was very different from fridrich then that might explain why your transition was so difficult. most beginners use LBL, which makes for a very easy transition to fridrich.
also- what is repetitive about fridrich?
If you want to get fast, learn Fridrich. Nearly every good cuber uses it. Needless to say, that's not evidence that it's the best method, but if the best cubers in the world use it, it should be good enough.
Petrus and Roux are also good methods, and both are used by several very fast cubers. Roux is especially notable because it requires very few algorithms to learn.
petrus and roux easily have the potential to be just as fast or faster than fridrich. at this time, there is very little research about the potential of roux and petrus, since so few people use it. however, if you(cubenoob123) are having difficulty with cross-building, then a block building method like roux or petrus might be a little hard right now. however i would highly recommend looking into both methods once you gain a better understand of the cube.
as for memorizing algs: just do it over and over until you can do it without looking at the sheet, then do it over and over until you can do it without thinking about the sheet(anywhere between 15 and 50 times)