If I understand correctly, you have an Apex EdgePro with the Chocera stones, and that list of knives you put with the bullet-points. Your wife does the cutting, you do the sharpening. And you're looking to figure out the fine details. Yes?
Okay. Main point: you are using what is arguably state-of-the art NASA equipment to fire off a bottle-rocket. An EdgePro basically contracts the learning-curve on bench sharpening dramatically, although there are those who believe that it also undermines certain fine details that come from freehanding. This is one of those debates that rapidly turns into a fight, so let's let it go. The question is simply where the limiting factor lies, and in your case it lies with the knives, not the sharpening equipment.
My principal question to you is whether you understand clearly, i.e. can currently conceptualize with some precision, what the difference is between a 1k and a 10k edge. I mean this both at the knife's edge and in the cut, which are not the same thing. I do not mean to imply that you don't know anything: I am genuinely asking whether this is something you grasp strongly.
If you do get this, I would ask why on earth anyone in his right mind would want to put a 10k edge on a knife whose edge will promptly bend and degrade. It's just wasted effort, nice perhaps for a cut or two, but otherwise pointless. If you're sort of OCD and enjoy it, go ahead, but I'd rather read a book, if you know what I mean.
But I suspect you don't get this. Why? Because if you did, you wouldn't ask whether you should grind up to 10k as the set permits. That suggests to me that you don't really quite understand what the polish is for, and you're genuinely wondering whether it is best to apply it regardless. So I will continue on this basis.
Your knives will, with little exception, hold very little polish. I am, for the purposes of the post, setting limits as follows: below 1k (<> 250 or so) is coarse shaping, well above 1k (=> 3k, give or take) is polish, and in between is sharpening. On that basis, you use shaping stones to set up a decent edge, but the edges produced by those stones are in themselves too coarse to be of good value in a kitchen -- they are effectively badly-designed serrated knives. You use sharpening stones to produce edges that will be of excellent service in the kitchen. And then you use polishing stones to refine the edges so produced, for specific purposes, with specific knives and steels.
In the present instance, the crucial question is what value arises with polish. The answer is fairly simple: if your knife is extremely hard and of fine-grained steel, a more polished edge will leave a cleaner result in the food. So where does this matter? Where a truly clean-cut edge is a matter of genuine concern. For instance, to give the obvious example, if you intend to slice raw fish and serve it directly, you want the cleanest possible cuts. If you are into very delicate beauties in vegetables that you don't intend to cook hard, it can matter there as well. With meat, not so much: as a rule, you cook meat after it's cut, and cooking will alter those perfect edges, so it doesn't matter; if you want perfectly beautiful slices of roast beef, however, yes, it does matter. Okay, so this is what polish is for.
Now in order to get the results you want from the polish, the steel has to stand up to it. This means two things: it must be fine-grained and it must be hard-tempered. If it is soft-tempered, it will roll and bend while you cut, and all that perfect polish will rapidly be for naught. If it is coarse-grained, the polish will not work well, because it will just expose coarse nodules in the steel, and these will mean that however polished the edge, it will still operate somewhat coarsely.
The knives you have are both soft and coarse. This is normal. If you are making knives, there is no reason to use expensive fine-grained steel if you do not intend to temper it very hard, and in fact there are reasons not to do so. Think about building a wall: there is no reason to make a fuss about getting every stone to have perfectly 90-degree angles and die-straight edges if it's not going to be under some kind of special strain -- in that case, probably visual as much as anything (which is true with knives too). Just so, if you want an edge that will be durable and forgiving, i.e. soft-tempered and easily honed back into place, you don't gain a lick from having the finest-grained steel, and arguably you'll actually lose something, so you don't use that kind of steel.
Your basic Henckels, Wusthof, Sabatier, and so on knives are tempered so that they do bend under use, which makes them durable. When they don't seem as sharp as they were, you run them on a hone (a "steel"), and they come back into line. Making a knife that way doesn't require super-fine-grained steel, so they don't use it. And what that all means, finally, is that polish is largely pointless. Get them up to about 1k, i.e. good and sharp, and they're happy and in their element. The rest is gilding the lily, and frankly pointless.
If you would like to see what the point of polish is, there are quite inexpensive Japanese carbon-steel knives that are both very hard and very fine-grained. Buy one, take it up to the ultimate level of sharpness, spending lots of time getting it perfect, and see what you think. I suspect, however, that you will think that you now have a very expensive hobby on your hands, because you will now think all your other knives are dreadful and useless. This is the beginning of an addiction, in fact. If your Pussycat doesn't have any interest, I suggest that you shouldn't either.
What you do need, however, is a good sharpening steel. I don't use them, because I'm long gone in my addiction to hard steel, but I believe the Idahone is held to be the best thing going. BDL, if he hasn't slid into a coma trying to slog through this long post, will soon tell you which model is best.
Regards from Academia, by the way. I hope you don't miss it!