The spot device doesn't need to survive a crash, just needs to send out a GPS ping once every 10 minutes. ie to give a fix on where the crash is would be sufficient.
10 minutes isn't nearly enough. Remember you're talking about something moving at 8-10 miles per minute, 10 minutes, so worse case your solution will give a range about the size of Iowa.
You could increase the ping rate somewhat trivially. Look at what the trucking industry does to keep an eye on cargo. And in any event, the current 777 search area is how big?