whyIsloveHard

Shouldn't be an issue...possession is not a crime that prohibits petitioning a family member for a green card.
Edit: Although you should know the details just in case they ask anyway.

You can marry and AOS from here. Just remember, you cannot leave while undergoing the process this way. You should not need an attorney. Research, research, and research!  Read the guides, use the USCIS site and ask questions here. And, last, but not least, congratulations to the two of you!  We are happy for you!  

Thank you for expanding on that. 
Yes, but OP may not know that's an option. I thought I'd share. 

Nothing you noted suggests a need for an attorney or service. Follow the guide on VJ, read the forms and their instructions, and ask questions. If you still aren't comfortable, then look at outside assistance.
The process and its result will be your sole responsibilities, not that of an agency or attorney.

As other users have said, you can marry now and then AOS. If total financial cost is not an issue, then you can disregard the rest of this post. Chances are that cost-wise, CR-1 might be cheaper than AOS. The government fees for AOS is $560 more: CR-1 ($535 I-130 Fee+$445 NVC Fee+$220 USCIS Immigrant Fee) AOS ($535 I-130 Fee+$1140 I-485 Fee+$85 Biometrics Fee). CR-1 medical costs vary by country ($60-$300 range), but AOS Civil Surgeon (average) costs easily surpass that. If you already paid for a non-refundable plane ticket to leave the US, that would be money lost; but with the CR-1 you would need to buy a plane ticket to the US.

if i were you id file directly for AOS. you did not come here with the intent to adjust status and stay. you have proof (and more time to gather more) of bonafide relationship and marriage.
 
unless you want to go back home to tie up loose ends and file wither a CR1 or K1. timelines for both are very similar, and if you consider doing that, the CR1 is generally speaking the better option.

Hello there!
 
If you were issued a Social Security Number/Card you could have your fiancé add you on his bank accounts, car insurance, etc. It may also be an option for him to add you on his rental agreement or lease.
 
I was also on a second J1 when my husband proposed unexpectedly and we decided to get married. My particular circumstances inclined me to take the CR1. I needed to return home finish my degree, this also gave me time to gather my documents (birth certificate, police records, etc.). Luckily I was able to visit my husband multiple time using my B1/B2 visa which I had from before my J1s.
 
A dear friend of mine who was dating an American US Citizen was on her 1st J1 when her boyfriend proposed and they married. Her case is somewhat similar to yours as she had been dating this guy since they met in Peru for about a year or so. She had no issues adjusting status. And she didn’t even use a lawyer: she proved her bonafide with lots of pictures from the time they were dating, and photos of her visiting her soon-to-be in laws at the time.
 
I hope these two experiences help you feel more comfortable with your decision.

Many have searched the depths of internet and failed. lol. It doesn't come up because it is not a thing. 

If i were you, i would do AOS. You have enough evidence to prove your bonafide relationship. Even with K1 and CR1, there is no guarantee and there is risk in everything but in your situation, i think AOS is best option. Getting married is not an issue as you can do court marriage and get marriage certificate. Sooner the better as this AOS process takes time. You should also be prepared not to travel out of country until getting advance parole document. 
 
I wish you all the best, 

Except lots of people adjust from other visas, which is why this website has TWO sub-forums: 1. AoS from K1 and 2. AoS from Work, Tourist & Student Visas
 
J1 is a work visa. Read other J1 AoS threads and stop freaking yourself out. If you read interview experiences, you'll find practically NOBODY gets asked, "So what was your original intent with your old visa?".

I have yet to see 1 case involving the IR of a USC (such as a spouse).
 
Which should tell you something.

We provided pretty much the same stuff when we first filed (one joint bank statement, one joint cell phone bill and some letters from family and friends). I personally don't think text messages and phone calls are necessary. They want official papers and they don't have time to read pages of personal text messages. You'll have time until the interview to get more evidence. We had a lot more at ours and our officer gave some of it back because he said the folder couldn't handle any more papers in there.

Hi, you will have no problem to do AOS without leaving the country. 
But of course you can choose to do K1 or CR1. Its 100% up to you:) 
 

They won't care about your original plans to go home. The I-130 instructions say to provide proof of bonafida marital union, not proof of your original intent to leave the US.

With all due respect, I think you have the answer you are looking for. People with experience have given you their advice. You can marry and file AOS. As others said, intent is determined at the border and should not be an issue now. 
 
Proving a bonafide relationship is what you should be focusing on. Read the guides properly and make sure you answer each question fully!

My wife and I were the same way. She was here on F-1 for 2 years even after we got married. After our marriage and before we applied for AOS, she had 3 visits outside the country (1 with me). Intent never came up at the interview. Just telling you this so you feel more comfortable about the intent issue. 

 
 

No issue marrying and doing AOS now. Intent was determined at the border. You just can’t leave and return to do AOS.