Thanks for clarifying the numbers earlier.
FWIW, this is my personal take on it, based on my experience with Height channels and dipole/bipole speakers. At one stage in the development of my HT, I was not using monopoles for my height speakers because the manufacturer of my main speakers did not make a suitable (smallish) monopole for the height channels and I am of the belief that the voicing of speakers is important in creating the overall sound field in a convincing way. Consequently I used dipoles, set to the bipole mode, for my height speakers. I asked Audyssey specifically what their views were on this because they recommend direct radiators for height speakers. Chris replied that they had not evaluated dipole/bipole speakers for height channel use but thought they would "probably be OK". I used the bipoles for some time and was always satisfied with the sound, as they were a) voiced the same as my mains and b) the height 'effects' are fairly diffuse in nature anyway. Later, I changed my speakers and the manufacturer of my new speakers did indeed have a suitable direct radiator for the height channels and so this is what I currently use. I cannot say with any degree of certainty that one was better than the other - both give a useful, pleasing effect. As a result, I believe that you could use either type of speaker for height duty and be happy with the result. I cannot say the same for omnidirectional speakers as I have no experience with omnis at all.
I would say that in your room, you are unable to achieve even an approximation of Audyssey's recommended locations for the height channels, so you might prefer (as I do) to use Dolby PLIIz for your height channels, as Dolby's placement recommendations are far les stringent than Audyssey's. My height speakers are up close to the ceiling and a little outboard of my mains. Remember, it is OK to mount height speakers on the ceiling if this brings them more into line with Audyssey's recommendations, but such an arrangement has a very low WAF. PLIIz derives the height information from the surround channels whereas DSX derives it from the front L&R channels and this may be one of the reasons that the placement requirements for both differ. I also found that DSX messes with the surround channels in a way I did not like, whereas PLIIz does not - YMMV on that. Also remember that Height (and wide) speakers are not part of any recognised 'standard' so their use is going to be a matter of preference and there is no right and wrong at this time - nor will be until/unless content is specifically created for these channels. This means that, really, whatever sounds good to you IS good.
WRT to side surrounds, I have used monopoles, dipoles and (now) tripoles. Each iteration has resulted in, for me, a significant improvement in envelopment. Bear in mind that I use my HT ONLY for movies and do not do any (serious) music listening there. Some people say that for music, monopoles make the best choice for surround speakers. My own view is that dipoles/tripoles are much better for movies and provide that overall immersion in the sound field that is desired, without excessive localisation of the surround channels. The tripoles have the benefit of good localisation when the content specifically demands it, but give terrific ambiance and envelopment otherwise - the best of both worlds. My surrounds are placed at 90 degrees to the MLP, but there is some latitude with this and you can place them rearwards or even forwards of that position - in fact if I had rear surrounds I would probably move my surrounds forward a little to help create the 'bubble' more convincingly. I do not have rear surrounds because my MLP is unavoidably close to the back wall, as yours is, and I do not feel that I can position rear surrounds effectively as a result. I have toyed with rear surrounds in the ceiling above the listening positions, but not carried it through (yet) as I remain unconvinced of the efficacy of such a non-standard location. I would prefer no rear surrounds at all to rear surrunds that might mess with the 'bubble' I have worked hard to create. Again, YMMV. I would, ideally, move my current tripole surrounds to about 110%, placing them slightly behind me (in the absence of rear surrounds) but this would bring them closer to the back wall than I think is desirable. If my room was deeper, I would definitely try this and see what effect it had on overall envelopment, but then, if my room was deeper I'd have rear surrounds, so the point is circular really.
I have no direct experience with wides because my room cannot physically accommodate them, but I would say that it's important to remember that Audyssey's recommendation for positioning is just that - a recommendation. You might find that conventional direct radiating wide speakers would work well as wides if you placed them where you currently have LH/RH marked on your diagram (but obviously at ear level). If I was determined to try wides, this is where I would put them to test their efficacy.
I have no experience of omnidirectional speakers at all but personally I would avoid them on the grounds that I have never really seen them recommended for side surrounds over dipoles and for rear surrounds over direct radiators.
I don't know if the above has served to help or to confuse, sorry. But my comments are based on actual experience (except where stated) and in a small, difficult room similar, conceptually to yours, sharing many of the placement difficulties. If I had to come down hard with a recommendation, it would be monopoles for the heights, dipole/tripole for the surrounds, monopoles for the wides and monopoles or bipoles for the rear surrounds - but there is no right and wrong answer here and I am sure others will have different views. Some of it will be pure preference (as I have for dipole/tripole surrounds - albeit a preference that is supported by various 'standards' such as THX etc) so given that, the only way to be sure to get what YOU want is to try different things. Problem with that is that experience is a great teacher, but the lessons are very expensive
If I can help any more (if I have helped at all!) then don't hesitate to follow up with more questions.
I'll need to digest all of that after Thanksgiving, but it is helpful. Thanks.