Hi Mal,
It is definitely a different approach to MSU. I really like the theme of the army and I think it would look great on the battle field. Hopefully we can see some pictures of it, either assembled for the battle or even some snap shots from the game!
Let me try to go through each choice one by one to see if I understand what you are aiming for with that army.
The Prince - Not as good as Alith Anar of course but as you said, since Special Characters are not allowed you have to come up with your own. He will do well with his Reaver bow since he is BS7. It is huge difference in comparison to Noble version with BS6. I used to run BSB with it and I quickly found out that more often than not his efficiency is limited due to 4+ to hit in many situations (move, long range, multiple shot to begin with). Potion of Strength is very handy with or without the bow so that there is a lot of flexibility here. MR(2) is an interesting choice, since the theme is to avoid combats and keep moving and shooting then it is a good choice. And it helps his unit too! Since you have some points left I would consider halberd. It is very flexible weapon, S5 is better than S4 and you keep the re-rolls. And it is also important where it is worth risking taking the charge where you would have stand and shoot with reaver bow in particular when you also used potion of strength.
Archmage - Since you plan on moving around a lot, giving your mage a steed is a good idea, especially with 3 fast cavalry units there. He has a nice equipment although for a single caster I personally prefer earthing rod. It might be due to some really crazy behavior of my archmage and loremaster though
Choosing Heavens is very interesting choice indeed. This magic was recommended to me before but I have never had a chance to try it myself yet so I cannot speak from experience. It looks to me as a good magic lore that does not seem to be that overwhelming. Of course, well timed comet or chain lightning can do quite a substantial damage. On the other hand, iceshard, harmonic convergence and even curse are all very useful too. I would be very interested in seeing how this lore helps your particular army.
Eagle Riders - you said you have 3 of them so it seems you forgot to add great eagle mount to BSB. I find the mundane eagle riders very intriguing. They are like flying knights indeed with 2+ armor save. They are still vulnerable but I presume that if you base them on 50mm bases then they can at least start the game with reavers?
I was just wondering on the role of BSB in such an army. You prefer to avoid combats, so I think he will be helpful when you want to rally reavers for example. Or simply adding that +1 to the combats you are going to fight in later turns to grab more points. Would love to know your thoughts on his role in your army though!
Reavers - I have seen units of 10 Dark Riders and they are very useful. Unfortunately, reavers do not have repeating crossbows and can't have shields so I think you will need to focus on avoiding combats even more than dark kin. They will do great in hunting down some support units of the enemy and I guess one of the main roles would be to provide hiding place for the archmage.
Shadow Warriors - can't have the theme without these guys! Just a pity it is just a single unit. Is it due to lack of points? Or do you need other units/characters more? I would love to see two units of these guys so that you can limit vanguard of the enemy better and have two spots for your Prince to go to if you choose to do so.
Skycutters - that is very unexpected here but I think it might be great addition, not only due to all the fliers you already have. I believe the bolt throwers may be a very good addition too. Perceived threat is sometimes as good as real threat. People would need to take into account the consequences of exposing flanks to these bolt throwers even if more often than not they might need 5+ to hit. They also bring some versatility due to the fact they are chariots and can hit relatively hard. With 3 eagle riders you might actually isolate some targets and attack from above to great effect. Of course they will need to be used with caution due to their fragility.
Swordmasters - Interesting to see these guys here! Are you going to convert some models to fit the theme better? They can indeed be a good protection for the repeaters. However, they might be still vulnerable to skirmishers and fast cavalry with some shooting abilities. They are cheaper than cavalry but I wonder if small unit of silver helms would not be better here? They could also act as help in combats. Don't get me wrong, I am great fun of Swordmasters (surprise, surprise!) but I fear they might be quite vulnerable. Fluff wise they are of course fantastic for this army!
Bolt throwers - well, they are the "shooting" part of the army. Very popular for a reason. No wonder you want to protect them too since you took 4 of them. Can make the advancement of the enemy even more careful and I think it supplements fast units well. The enemy may have difficult choice to make if they want to chase your fliers/cavalry as it may force them to expose their regiments to bolt throwers. 4 of them can make even the toughest fliers shy (unless they sport some silly 3++ ward save). And with fast moving army in general, you should not have problems in getting clear line of sight.
In general your army has a decent number of drops so you may try to outdeploy the enemy. Vanguard for 3 units (unless joined by characters) can further help here and the fact you have 3 eagle riders can help to fool the slower enemy and change the direction of the attack. You will try to move around and pick only the fights where you can win quickly. It is possible with fast moving army but since your units (and even characters) are fragile you have to make sure there are not many attacks back.
You may have tough time against small arms in good numbers. WE or DE with their glade guards and dark shards may be a problem. However, being patient and being able to cast some thunderbolts, chainlightnings and comets may help to tip the scales into your favor. I think you will need to be very precise with movement even if your army is fast. Simply because if you go to the open these units can be quickly destroyed. Also, anticipating the moves of the enemy will be important to position reavers for their feigned flight.
I think the enemy might try to hunt down the Prince as he may seem to be vulnerable. He can operate alone though (risky but sometimes doable) and I would love to see him doing that too! But in case the enemy has means to do so (magic missiles, shooting etc.) you definitely need to find a safe spot for him. One thing I was wondering about is that when he operates solo he may use terrain to much better effect.
The challenge you may face is that this army is good at avoiding and shooting but it may be hard to get points. 4 bolt throwers will do damage but not always enough to kill entire units, in particular cheap infantry. You may have trouble in getting the points from damaged regiments but fortunately you have fliers to hunt them down and your archmage can help here too.
This army is not as nasty as similar version of DE with warlocks, dark riders, bolt throwers and peg riders so hopefully your opponents will not complain about it. However, I would expect that to happen sometimes as in general, armies that shoot and avoid combat are not liked.
I am looking forward to reading about some games with this army so hopefully there will be some reports in the making in the future.
Cheers!