Simple solution...

The Innkeeper loads all his worldly possessions and cash in a cart, puts a sign on the front door stating "I'm leaving it as I found it...take it...it's yours" and goes Galt.

Easy-peasy

You're compounding several things into one problem. First, the solution chosen by the innkeeper worked for everyone, including Joseph and Mary. Second, the shepherds visited the manger, but the magi visited when Jesus was a toddler, probably about a year old, and by your own admission, Joseph and Mary weren't in the inn at that time. That suggests that Joseph and Mary had to accept some emergency charity for a few days, but were productive enough to make it on their own by the time the magi arrived. This is supported by the fact that Joseph worked as a carpenter as a career, so he wasn't your typical welfare recipient. Being Jewish, I'd have expected a better presentation than this, especially from someone who claims to have read the Christian Bible well enough to be able to connect the dots better than this.

With all due respect you need to understand the context and concepts here...
It is March/April (lambing season) in Judea.
Most traveling folks at that point can "camp out" and avoid a need for shelter.
Joseph showed up at the Inn because Mary had "broke water" during the journey and Joseph was needing some privacy to deliver the baby.
The Innkeeper's wife was the person who intervened on their behalf and opened a private place for delivery.
It isn't so bad...a manger is a place for the hay so that the cattle can eat.
It is a soft landing.

First come first served. That rule is often avoided if a tip is involved.
The lefty problem is the "each according to his need" dilemma. If strictly followed puts the less needy in second place compared to the needier. This creates an incentive to be needier or at least to appear to be needier. If you are against that you have no compassion and you are a heartless beast. I know. I have been operating without a heart for many years.

I see charity work sort of like a producer, seeing a need and supplying the means for it to be met. And not by just giving a temporary fix, but by finding the root cause of the problem and fulfilling it (ie, finding someone that can't find a job because he/she has no skill and teaching that person a skill, rather than throwing money to that person) I think that Ayn Rand would acknowledge that if someone is truly a producer, he can interweave any charity he CHOOSES into the things he produces, IF he CHOOSES to provide any charity at all.

The allocation of scarce resources problem.
Those who say it should be done by need, do not think it thru,
Who determines the scale of the need?
In this case it could be the innkeeper, he had better work out strict criteria or he will soon end up in need himself.
That can work ok on the face of it. He can make his own rules to choose between the pregnant woman, the carpet salesman, and the elderly with consumption needing protection from the cold. That is the micro view.

The macro view is that all inn-keepers will find an increasing demand for rooms by needy travelers, some being caught out by events, some will start a journey relying on being able to demand accommodation.
Soon Caesar will require that the needy be looked after, innkeepers will then have to break contracts with those who have booked and can pay. The tourism and welfare department will set the rules for selecting among the needy to accommodate and from those who can pay but are not needy enough and are to turned out or turned down. There will be prosecutions and court cases.
Lots of job creation in the public sector and court system - But see the 'broken window fallacy'.
All those extra jobs are to be paid for by the carpet salesman and the innkeeper in taxes, and note that their gross income goes down.

So let's look at the real problem: government! The Inn was sufficient for its normal patrons. The problems of overcrowding were caused by Caesar Augustus' decree that "the whole world should be taxed" (meaning the Roman world of which Israel at the time was a vassal state).

This is just one more example of government meddling causing problems in the free market. =D

first...poor planning on your part does not constitute an emergency on my part...
second...if you have perfect knowledge and know the birth of this child will result in Mohammed, Jesus, or Hitler would you be justified in taking a life to save millions of lives down the road???...

The article is full of Christian in jokes that I only partially get. :)

If the inn keeper had been astute, he would have foreseen the new tax law would cause an influx of people from out of town and would have raised prices to the point there would be a room available for anyone who wanted one and could pay the high price. Then people could decide if they wanted to split the cost with another traveller or pay the high price for their own room. If this happened on a regular basis, the high rents would entice people to build new inns or rent out rooms of their houses in future years. Maybe there were anti-price-gouging laws that prevented that. I know nothing about the real answer but my wild guess is value was so closely tied with lang in that region that they had no concept of moderm markets. 1 acre of land was 10 oz of gold, in their minds, and from that one night in the inn was one-tenth oz of gold, and thoseo were wrongly seen as immutable laws of the universe.

so see a real live virgin birth would have been worth the loss of a nights revenue. Imagine the advertising value

Old Dino has something to say and what Old Dino says is this~
A woman having a baby ain't gonna voluntarily give up her birthing space.
Not for nothing. Not for nobody.
Not the Virgin Mary.
Not Bloody Mary.
Not any Mary in between.
It ain't gonna happen.