5 million meters per second is way too fast for the slow journey. If you continuously accelerate at one g then you can solve ##d=\frac{1}{2}at^2## for time and discover that it will take you about two and a half hours to reach the moon. Then you can use ##v=at## to calculate that your impact velocity on the moon would be about 90 km/sec.

A more realistic journey would spend half the time accelerating outward and half slowing down on the approach. That would take about three and a half hours total with a peak velocity of a little over 60 km/sec.

Still, 120 km/sec total delta V is well more than we have at our disposal. The actual trips to the moon involved peak velocities that were a small fraction of that. For efficiency, the burns are kept brief, using just enough fuel to make use of Hohmann transfer orbits.

Extreme acceleration seems to be not much use in any circumstances, in fact. Your point about a Lunar mission is well made. If the plan is for a very long journey then the acceleration time (at both ends) is a small fraction of the total journey time so what would be the cost / benefit situation of subjecting passengers to hideous conditions in order to shorten a journey of many years by a few days / hours. And there's the Energy budget to consider.
Of course, if there were some system for Regenerative Braking . . . . . . . . (only joking')

When you told about that uniform, I thought about a hypotetical situation. So, a human accelerates with the same 20,408g. It moves her with increasing speed, but the same force affects her body. A hypotetical costume diminishes the force that affects her body. That 20,408 g that would've destroy her otherwise.
Would she still move in space, or will just stand dead on her tracks?

Have you been reading al the above comments?
We have been pointing out the lethal consequences to bodily liquids and tissues at that level of acceleration - with or without 'Anti-g' measures. How can you then suggest the traveller would be in a position to move about? She would be DEAD.

All costumes produced to date obey the laws of physics, one of which is F=ma. If the costume reduces net force then acceleration must also reduce (assuming that the wearer refuses to be cut into small pieces with reduced mass). There simply is no way to reduce net force and keep high acceleration.

Newton's second law says F=ma. There is no magical pixie dust exception for fancy costumes. Your acceleration is determined by the force on your body.

The best one can do is to try to spread that force out evenly so that the associated stresses are not too extreme (g suits, recumbent position, water bed, liquid breathing, etc). But 20,000 g's is too extreme to mitigate that way.