Okay, so no "Reptile Specialist" has seen him, but a general vet...I agree with the MBD diagnosis, but something isn't right here, it could very well be parasites, quite a few babies come home from pet shops and breeders with parasites, and if they are not treated they just continue to multiply.
If he happens to have a parasite that is hosting on his nutrition, like a high count of Pinworms, they have been and continue to eat every bit of food/nutrition he's taking in. That's the issue. So without a simple fecal test you have no way of knowing what parasites and/or protozoan infection he has, what counts/loads they are in, or what medication to use to treat them. And if it's a worm that is stealing away every bit of nutrition from his GI tract before he is able to metabolize it, he's not going to make it much longer, as small as he is. So you need to in the very least drop off a fresh fecal sample to that general vet you already saw (who by the way should have already done this, she is very capable of doing a Gram Stain and a Fecal Float Test, she does them on dogs and cats every day), and then seeing what parasite and/or bacteria/protozoa are in moderate to high counts and prescribing the correct meds (DO NOT ALLOW THE VET TO TREAT HIM FOR LOW COUNTS OF COCCIDIA, IT'S NOT NECESSARY AND WILL ONLY MAKE HIM MUCH WORSE, ONLY MODERATE TO HIGH COUNTS NEED TO BE TREATED).
If he tests positive for moderate to high counts of Coccidia, he should be put on Toltrazuril for it, and for Pinworms/other worms in moderate to high counts he should be give Panacur... DO NOT ALLOW THEM TO PUT HIM ON ANY SULFA DRUGS OR IVERMECTIN!!!!
In the meantime, as I already mentioned, no more soaking him, he could aspirate water into his lungs that way, and it's not
hydrating him at all, only stressing him out. They must take in AL of their
hydration through their mouths, so in addition to feeding him the Oxbow Critical Care or the slurries you're feeding him, he needs to be given the Pedialyte (better than water at this point) by either dripping it on his snout and letting him lick it off, or by force-feeding it to him, you're at that point now that you need to force it, several times a day. Do not waste Pedialyte by putting it in a "
bath" for him to sit in, as unless he's actively
drinking it through his mouth in the
bath he's not getting any of it in him at all.
Are you using a Digital Probe Thermometer or a Temp Gun to measure his Basking Spot Surface Temp? Or are you just reading the Hot Side Ambient (air) Temperature off of a stick-on thermometer that is stuck to the glass on the Hot Side of the tank?
I'm asking because a baby/juvenile Bearded Dragon normally, when healthy, needs a Basking Spot Surface Temperature between 105-110 degrees (110 degrees is the hottest temp that he should have anywhere in his tank at any time, over that is lethal, but babies and juveniles under a year old need to be basking on a Surface Temperature between 105-110 degrees for at least 13-14 hours a day, and the Basking spot/platform that you use as his Basking spot needs to be directly under both the UVB tube and his bright white basking light, so they need to be right alongside each other, so he gets both at the same time while basking). Your Basking Spot Temp of 95-100 is not nearly high enough, especially when he's sick. So please, lower the bright white basking bulb down a few inches towards him (DO NOT MOVE THE UVB TUBE AWAY OR HIS BASKING SPOT AWAY, ONLY MOVE THE BASKING BULB CLOSER TO HIM TO BUMP UP HIS BASKING SPOT SURFACE TEMPERATURE). Then wait about an hour for the temperature to heat up, and remeasure the Basking Spot Surface temperature with either a Temp Gun or a Digital Probe Thermometer, allowing the Probe to sit right on the basking spot/platform for at least 20-30 minutes before reading it, so it heats up to the actual correct temperature. Keep moving the bright white basking bulb down towards the basking spot/platform until you get the Probe to read between 105-110 max.
Also, you say your UVB tube is a Reptisun 10.0 T8, but you say it's 22" long and in a 24" fixture, so that would be a T5 UVb tube...if you did actually order the 22" Reptisun 10.0 T5HO UVb tube and a fixture for it that's great, but make sure that's what you got, if the tube is actually 24" then it's the T8. but if it's only 22" then it's the T5HO, which is what he needs right now.
Please, call up that general vet you already saw and drop off a fecal sample ASAP. He really does need to see a very experienced Reptile Specialist vet and not a general vet or an "exotics" vet at this point, this has been going on way too long and he's not going to make it much longer this way, but that general vet can certainly do fecal tests and prescribe medications...
I suggest however that before you give him the meds prescribed by a general or exotics vet you check here first and let us know what they gave him, because a young baby was just kill a month or so ago by getting a Sulfa Drug prescribed for Coccidia by an "exotics" vet with no idea what they were doing, so if it's not a Reptile Specialist, it's always better to check first...