Attempting to catch up and respond to any lingering questions.
Welcome MilfordFound and lackingimagination!
Can't believe I missed out on the dressing table porn 
still have a giant folder full of reference pics from when I last designed mine.
Othersideof40, please be careful with any new products, especially masks. Make sure they don't contain any common irritants (fragrance, essential oils and fragrant compounds, synthetic dyes/colourants, alcohol den., chemical sunscreen filters) as your skin is in a fragile place right now. As an aside, masks are fun but their effect is really temporary, esp. wrt dehydration.
Wrt facial oils, tackling dehydration due to a compromised skin barrier is a two pronged strategy. You need a humectant like HA to replenish and retain the moisture levels that are depleted due to the weakened barrier of your skin that would otherwise hold this in and you need an occlusive to trap that all in, acting as a surrogate barrier whilst your own barrier attempts to regain its strength. Facial oils are oft described as occlusives but in reality very few actually have the density necessary to inhibit Trans Epidermic Water Loss (TEWL). Petroleum Jelly has the highest TEWL ranking, but it should only be used if you're currently not reacting to anything, as its strength, the ability to trap in ingredients then actively works against you.
Dependant on how severe the dehydration determines what kind of occlusive you use alongside a humectant. In your case, it would be at the more severe end, so if you can tolerate Mineral Oil derivates, consider using Vaseline as a final layer at night (its heavy occlusive properties may interfere with SPF efficacy during the day if using a chemical SS). Squalane is a good alternative, slightly less heavy but has good TEWL inhibiting properties. Can't remember who asked specifically about Squalane, but yes, I think it's a good basic ingredient although it often gets mixed of with Squalene which is shark derived but has similar properties.
Bagel, yes the Hada Labo Premium Lotion is good for severe dehydration. I'm always more hesitant with the standard HL lotion as it can break some people out terribly. I tend to prefer the Kohaku-Hada Lotion (the Amber version) as its INCI is a lot cleaner and I've seen less feedback of horrible breakouts.
user, as yong already pointed out neck & cleavage don't really require a specific product but since you're more sensitive there perhaps just a no nonsense body lotion like LRP Lipikar may do the trick? You could also try a Urea based cream, like the 5% Urea from Eucerin (for the face). Not a full blown active but with a bit of exfoliating properties as well as being a good humectant.
The Avene Extremely Gentle Cleanser Lotion isn't discontinued according to the French Pharmacies I visited where I asked as I didn't want to buy and test out something that was on its way out. The very popular Gel cleanser was discontinued late last year. It's still available on the French e-commerce sites too but there does seem to be a change out as they had a value version of 300ml for a while and that seems to be on its way out for the standard 200ml so on certain sites it shows up as sold out for the 300ml but they will have the 200ml version.
Milford, how long have you been using the Olay as this also contains a relatively high % of Niacinamide (they're the ones who've funded most of the research on it). It may very well be overload as you've got 10% + approx 4-5% (which is fine on its own) from your moisturiser.
Are you taking up your SPF around the eyes currently? It may very well be that the high alcohol content in it is adding to the dehydration. The Kiehl's Avocado Eye cream mentioned above is a 'nice' eye cream for those who just want a separate product there but it's best suited for drier skin rather than dehydrated. Nothing strange going on health wise? Dry eyes (predominantly the eyes themselves but the ocular area around it too) can be a sign of Vitamin A deficiency. Product wise, Hylamide SubQ for eyes is probably your best bet although I would give it some consideration considering it's another Deciem HA product.
Just from personal anecdotal experience this summer, I've found that cutting out TO products with HA in it (just using the Retinoid now) has pretty much stopped me being dehydrated where it usually ramps up a lot in the summer time. We've seen this before with TO, specifically with their HA 2% + B5 causing dehydration rather than giving hydration. It could possibly be the L-AA format of Vit C that was possibly causing it with me but I've never had issues with that in other L-AA products and since Deciem is a big fan of Low Molecular Weight HA I think there is something to it there (the expert scientists tend to argue a bunch about LMW vs. HMW and there isn't much consensus - However, it may also be down to Deciem's formulations as the HL Premium Lotion has a whole bunch of LMW, MMW, and HMW HA forms in it and I've yet to see any feedback on that ever dehydrating anyone).
I do think it's sensible at this point to take a step back and simplify your routine a bit and get a hold of the dehydration issue. The double cleansing with two oil cleansers (as opposed to the more 'ideal' combination of oil followed by water based cleaser) probably isn't helping much either. So adding in the LRP Toleriane Cleanser or the Avene (mentioned above) would be good and I'd even consider using that as a single cleanser (used on its own or twice if necessary) for now as unlike the UB and BS they're not fragranced and since your skin is feeling irritated at the moment it's best to avoid further irritating it. This also goes for facial oils with possibly essential oils in it.
For AB toners see above but I think the Benton Snail Bee High Content Essence may work well for you too but be mindful of product overuse. The AB hydrating toners are basically like an HA serum like the TO HA and Buffet, just much better value and slightly more watery. The Benton is thicker though, much more serum like despite the essence name.
I guess you haven't gotten to the thread where the discontinuation of Toleriane Ultra Fluide moisturiser was announced and mourned, you can still find it in places but it is a 'light' moisturiser so if you need something heavier the Urea 5% mentioned above also could do the trick. Otherwise, I tend to rec the Eucerin UltraSenstive for combo/oily skin in its place, but some people were having trouble tracking that one down in the UK too so not sure on its current status.
lackingimagination, have you had a read through of the info sheets in the OP yet? If you can lay out your current issues and where you're getting stuck I'm better able to respond 
mint, just spray the Bioderma in your hands, then apply as normal. It's a faff but works fine, it's not an aerosol type spray.