Leavingtofate

I've already got a job offer. I thought it will give me a higher chance to enter the US if I can show the immigration officer my job offer letter

That's a bit harsh: she was fresh out of college, by no means "married" to the USA, and chose the easier route. That's not that surprising especially given the fact that she has a citizenship of another first world country. Not like she had to go back to Russia or Ghana (in which case I'd absolutely pick a job in service industry). 
 
My $0.02. 

No, why should you? You could get lucky. Worst thing that happens is you’re given voluntary departure. 
 
As one recent American used to say what do you have to lose? Good luck!

Sounds like a plan! Once in the US, get state ID or DL from DMV. Showing it for I-9 accompanies by unrestricted social security card will help mitigate any issues due to expiring GC. You wouldn't have to show your employer soon to expire GC. Renewals take forever nowadays, and you don't want to employer to jump up and down asking for up to date GC in a year or so.

Jump on a plane or stay is your options

I know what I was thinking at 22:
 

 
@Leavingtofate I think you can only fly to the US and take a chance. You better do it sooner than later. I wouldn't even leave your current job if they allow you working remotely. 
 
Open a bank account, you can open many accounts online nowadays, especially if you have SSN. Provide your sister's address for debit card to arrive.
 
Search for a place to rent. A sympathetic CBP may let you in if you demonstrate enough efforts to establish life in the US (of course not guaranteed).

VJ record is 9 years.

Thats what USC’s have to show to qualify to get their spouses home.  Working overseas is specifically listed in the “abandonment” column for LPR’s. So is skipping taxes. 
You’ll either slip through at the mercy of an IO or face a slam dunk in immigration court.  This is the reality of where you are right now.
I know for sure it is.  We are not misaligned here.

The nasty note said “out 11 months”.  I saved it as a USCIS souvenir 
I think this one is going to go to court though to be honest. 

I'd say there is better than 50-50 chance that you will face heavy scrutiny.  It certainly could be seen as abandonment.  The only way to find out is to enter the US.  CBP cannot force you to sign an I-407, but they can refer you to an IJ.
Extended absence.
No taxes filed since receiving Green Card.
Previous Warning
No other actions to maintain residency.
 
 
 
 
 
 

I really do.  I filed with foreign earned income using turbotax for several years.  Just follow the menus.

This is tough.  An SB1 would be summarily denied.  Your ONLY chance is to fly in on the green card, dig your heels in at secondary, and do not under any circumstance sign away your green card.  You need to prepare something to show as many maintained US ties as possible and you need to catch up on filing taxes. You can be treated as resident for tax purposes and exclude foreign earned income and likely won’t owe anything anyway.  I hope you make it but it’s possibly going to be tough.  Good luck.

With a previous warning, yes the chances are high they will issue an NTA. I don’t see from the post you have maintained any ties to the US or how you will demonstrate you never intended to abandon your LPR status.

Thank you for the suggestions - I will try opening up a US bank account. I think once I have the US job offer, I will hand in my notice for my UK job and hopefully showing this to CBP would demonstrate that I'm serious in taking up the job offer in the US. Will also definitely find a place to rent before I leave for the US.