You can apply now. You need to stick around long enough for your biometrics appointment which will be approximately 30-45 days after you apply. You can request that the approved document be mailed to you overseas.
Disclaimer: This answer is for informational purposes and does not take the place of a consultation with an experienced immigration attorney. This answer does not create an attorney-client relationship.
You might not need a re-entry permit if stay is for less than one year but multiple stays out the country amounting to one year or more might pose a problem especially for citizenship.
This answer is not intended to replace a consultation with an attorney and does not create an attorney-client relationship.
Your physical presence history in the US denotes someone who just obtained the green card to "have it in his or her pocket" but has no intentions (or ability) of really residing in the US. Contact an experienced immigration attorney before it's too late. Most of us, myself included, offer consultations via Skype.
Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.