You can apply for asylum until a year after TPS ends, and still be within the one year filing deadline. So, I don't understand why you want to file for asylum now. If there is not a huge threat to you when you return to your country, just stay on TPS, make trips back home to have quality time with families.

Asylum, and TPS are totally different immigration benefits.If you already have TPS EAD, it might only delay your asylum date. It all depends upon your luck, and your mental strength. So, use your TPS EAD to enhance your career, and apply asylum if you are eligible.
kehi chij pauna, kehi gumaunu parchha..you know what I mean.
Good luck !!! and enjoy south california