How can God be completely just yet completely loving at the same time?

Imagine you are a criminal and your father or mother is a judge in court.

Your parent may advice you when in home, when you get charged or brought to court for some reason, your parent has to do the role of a judge.

Read Job's story.

I applaud you looking at places where a purportedly all loving God would allow slavery or call for someone to be executed for picking up sticks on the wrong day would make people question why this is. 

However, you want people to refrain from certain possible answers?  Why?  I can appreciate if you mean you aren't looking for them as simple one line answers.  But, unless the only thing your really interested in is fortifying your own confirmation bias, those are on the table for actual serious inquiry. 

The bible frequently makes claims God is a God of love.  But, there's no shortage of Yahweh ordering war crimes, or directly committing genocide by flood. 

1 Samuel 15:2 The Lord All-Powerful says: ‘When the Israelites came out of Egypt, the Amalekites tried to stop them from going to Canaan. I saw what the Amalekites did. 3 Now go fight against the Amalekites. You must completely destroy the Amalekites and everything that belongs to them. Don’t let anything live; you must kill all the men and women and all of their children and little babies. You must kill all of their cattle and sheep and all of their camels and donkeys.’” 

Now, a lot of apologists will try to sweep that under the rug by claiming He is also a God of justice.  If you want to claim that fighting a war might have some moral justifiability. But, that really applies to humans that have no other option.  God could magically teleport the Amalekites to Madagascar with no suffering for anyone.  Yahweh is omnipotent, and as God he can do anything! If he were a peaceful and loving God, he would be able to correct bad behavior in a peaceful and intelligent manner, rather than ruthless killing of entire nations. So, some flimsy idea the order to murder infants is just?  Not buying it. 

And, I don't think the bible is really making the case for an omnibenevolent deity either. 

Isaiah 45:7 I form the light, and create darkness: I make peace, and create evil: I the Lord do all these things.

Explained in Romans 11:33-36.  Compare Jeremiah 9:23-24, Psalm 89:14.

When the Judge issues verdict of capital punishment to the criminal who slaughtered his own mother , did the Judge issue this sentence to the son, because of his hatred or anger or because of the love of justice. That is how.

That would not be too difficult for God because is anything too hard for the Lord? (Genesis 18:14) - the One who caused Abraham and Sarah to bear a son well into their 99th and 100th year of age respectively!!!!!!!!!! -  - the Lord God who created this world, universe and everyone and everything in it?  Just look at the beauty in the world and the intricacy for example of a human brain, an eye, a heart  - the Sun, moon, stars, galaxies, universes, animals with fur, birds with feathers, fish with scales, reptiles which are cold-blooded, insects which inhabit every crevice imaginable,  - besides, remember this - God doesn't see as man sees, for man looks at the outward appearance but God looks at the heart (1 Samuel 16:7)

It is precisely because God is so very powerful that it makes Him God.  We don't know His thoughts or His plans or purposes many times.  He does things in the opposite ways of mankind because His plans are perfect, His ways are unsearchable and many times they are past finding out.  I am GLAD God is so different from us.  I would have no confidence in a God who was like me.

When God judges, "Can a mere mortal be more JUST than God? Can a man be more pure than his Maker?" (Job 4:17)  GOD SEES RIGHT INTO THE HEART- HE SEES THE REAL PURPOSES AND MOTIVES BEHIND WHAT WE DO AND WHY.  No man can do this.  We might hide those things from each other and even from ourselves sometimes but all things are open to God - that's how we know HE ALWAYS JUDGES PERFECTLY AND RIGHTEOUSLY.  

Because those are One of His Beautiful Qualities,  He is The Most Just and The Loving-Kindness, The Most Affectionate and He is the Beloved as well and His Beautiful Attributes never changes.

God is Al-Wadūd, The One who loves, .  The One who is the source of all love and loving-kindness. The One who is deserving of all love and affection. The One who is the goal of the highest love.

God Almighty is also Al-'Adl, The Equitable,  The Impartial,  The Just,

The One who rectifies and sets matters straight in a fair, impartial and equitable manner.The One who always acts justly. The One who delivers absolute justice.The One whose wisdom of justice is based upon complete knowledge of past, present and future.

through the art of cherry picking

He loves the sinners but hates the sin like don’t fart in to many restaurants then run out Laughing 

Quite simply because He is righteous.

He cannot.

I hope this helps.

Well, the two things you bring up are not exclusive, you know.  Why do you think they are? It's like asking "do you wear black socks or do you bring your lunch to work?"