Adjustment of status through spouse

Yes, your USC spouse can sponsor you for a green card right away. Once your "green card" will be in your pocket, you will then be able to "withdraw" your pending asylum case. Don't do it before!

The recommendation of my distinguished colleague, attorney Giacomo J. Behar has furnished to you is correct. Now you just need to act on it with the help of local immigration counsel. You should not be restricted by geographic factors. Good luck.

If you are a resident after holding asylum, you do not need to apply for resident status again. You should consider applying for naturalization after you are eligible.

I do not understand why you would want to get a green through marriage when you already have one through Asylum. Is there a perceived benefit (other 3 years filing for citizenship) the marriage green card provides that the green card you already have through Asylum does not?