Unfortunately, Costa Rica has an extradition tready with the US - That means the Embassy would have to send you back.
You cannot get assulym from the US Embassy as a fugitive.
If you have to get back, then I suggest you will want to go to the embassy and turn yourself in. It's a free ticket home. However I suggest you will also want to contact a local attorney in Florida - who will be able to meet you when you arrive and then try to handle things.
There is no way they are going to just set aside a conviction and a sentence. You are a fugitive from Justice. So you will have to be in Florida jail until your attorney can try to get a new trial
, etc or whatever it is you are seeking.
Im sorry that it is not better news for you in this regard.
I suppose the only other option is to go to the Embassy and try to get the passport. Who knows, maybe nothing will come up. But the worst scenario is they detain you for extradiction.
If you happen to get the passport, then you only would have to be concerned with your point of entry into the States and if they will detain you in another state since Florida will not extradite.