I would normally tell you to renew the EAD at least, but there is no guarantee that they will extend beyond September 30, 2016 and I wouldn't want you to waste the $465. There might be a small possibility that they would extend it for a year, but I don't know if that small possibility is worth $465, especially if they don't extend the TPS. What that means is that if they grant the EAD for another year, but later don't extend TPS, the EAD is not supposed to be valid anymore, but most employers don't check. They just note that the EAD is valid for another year and won't bother for another year. Again, still no guarantee.
As far as getting back into H-1B, since it costs the same amount of money to ask for a change of status as to just file the H-1B petition, I would file it as a change of status and see what happens. I doubt that they will approve the change of status, but they should approve the H-1B petition. If they approve both, then you go back into H-1B. If they approve the H-1B petition but deny the change of status, then you would have to leave the U.S. to go for new H-1B visa stamping and use that to come back. If you have had an H-1B visa stamp in your passport before, then you should be able to go to Mexico or Canada for stamping. If you have never had an H-1B visa in your passport before, then you are supposed to go to your home country for stamping. Of course, if there is a very urgent reason that you cannot go, like it is dangerous, you could ask a U.S. Embassy or Consulate in a different location to process you. They normally do not do it unless there is a compelling reason to do so.
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