Ok....until now I don't see any real problem with your guitar. It is not unusual that new guitars don't have a good setting. Especially, majesties. I have three of them and it took them at least a year to get really "astonishing". However, they are of course good guitars immediately when set up properly.
Have you ever found a guitar properly set up up in a guitar store? I have not. This is for two reasons. First, those guitars are not properly set up second, there is personal preference.
Coming to the point now, this is how I prepare a new guitar.
1. Check stringe gauge and change to preference (not all of my majesties came with 10s)
2. Check string action. This is a tricky one and as mentioned above it is depending on personal preference. Unlike as told before neck adjustment is importend and directly influencing the string action but more on the first twelf frets. The saddle height or bridge hight is more relevant for the frets above 12. I like an ultra straight neck for example. Therefore, I eliminate the bowing of the neck until it is completely straight. This can be evaluated when pressing down the first and last fret on a string. If there is no space left at the 12ths fret, than it is at least straight. If no proper tones are coming out of your guitar in the lower fret region then the neck bowing to much in the wrong direction. If that is to my liking than I lower down only the particular string saddles so low that I get out a tone on every fret and without having to much buzz. I try not to lower the bridge to much but the saddles to get a more advantagious ratio of lever on the trem. I don't want force on a string to easily cause trem movement. This is dependent on string thickness, stiffness of trem springs and also the angle of strings in relation of the lever point of the trem. Stiffness of the trem springs is denpendend on the material, the thickness and also the state of elongation. So think of this before putting in more springs. Usually EBMM guitars come with the trem plate at the same hight as the body surface and that is estetically fine and also advantageous for string stiffness(for fast alternate picking[if the stiffness is to low you might accidently bend the string with your pick when stroking and the flow is gone]). That is basically the trick. You might have to re-adjust the neck once a week on majesties(the monarchies seem to be more stable) for a while until you get a very stable situation.
3. Adjust trem springs to the correct position of the trem plate.
4. Adjust the intonation with the intonation screws and start at point 2 again....

usually there should not be that much of a change. For intonation adjustments I use flageolette tone and fretted tone on the 12ths fret. It is important that you use your actual fretting pressure that you usually use for playing on the fretted tone to get accurate results. When that is okay you should try out lower frets; those can be divergent if the nut height is not optimal; however this rarely needs correction.
5. Put something into the trem springs to prevent their ringing which additionally gets picked up by your pickups! For that I use old clothes that I pull through using old guitar strings. This may impair the restoring forces of the trem springs a tiny bit but I think it is worth the price.
If all these points can be resolved you should be very satisfied with your guitar for a very long time.
Still, usually guitars are set up pretty badly. Actually, there is a rather famous german guitar seller who made the same discovery when he was young. When he asked his guitar seller if the guitars in the shop could be set up properly the seller just said that it is sensless and he does not know where to start. So.....don't expect to much. If you set it up your self might be even better fitted for you.
So congratulations on your new guitar! I think it will work just fine! Happy new year to everyone.
Regards, J