I would also suggest you applying for TPS, and EAD with it (if you don't have one already). Like Gundruke brother suggested, it is definitely a good back up plan. Another thing, Unless you are super lucky, Most asylum cases are being backlogged, and the waiting time frame is more than two years. Hope this won't happen to you, but if it does, TPS will benefit you in lot more ways. Like you can go to school paying only instate tuition. and definitely, AP to travel to india. Though its not recommended, I have seen people doing this and came back with no trouble.
As mentioned in USCIS website, and many Lawyers suggested, Tps will not contradict your asylum case, though you should be prepared to explain why you applied for TPS on your asylum interview, in case the officer ask you.
Good luck