I'm glad that Remi check-out well, but do make sure that you get the routine Blood-Work done ASAP, not only because you never know and you need to know, especially because he's not had it done before, but most-importantly so you have all of his normal, "Baseline" levels for everything when he's completely well, so that if he does become sick or something appears wrong, they'll have his Baseline-levels for comparison, as sometimes just a small-deviation in certain levels may be slightly "abnormal", but normal for Remi...
I'm a fan of Red-Palm Oil, just as long as you see clear, definite improvement within a few months of starting it, and just as long as your bird can tolerate it and doesn't show any signs of negative-reactions or illness from it. If you don't see any improvements in feathering, etc. within a few months of using it, then discontinue it, as the less stuff you give them the better...
***I'm not going to go into the reason why pet birds should not have an artificial UVB light over them, or why it does absoutley NOTHING for your bird in-regards to Vitamin D (UVB light does not GIVE THEM Vitamin D, that's a common mistake and is falsely-spread in reptile forums all over the internet), but I will definitely tell you that you that the brand, type, strength, AGE of the BULB, and UVB-output of the particular UVB light you have MUST be looked-at, as these are all factors as to whether or not they will provide much UVB light in the first place, even if it was beneficial to birds (which it's not), but much more importantly because over 50% of the UVB bulbs that are commercially-sold for birds, reptiles, etc. are extremely harmful and cause temporary and permanent Eye damage, Blindness, Skin Damage, Skin Cancer (Basal Cell, Squamous Cell, and Melanoma), Photoconjunctivitis in both eyes that requires high-doses and long-courses of Antibiotics to remedy, and most-severely are the Neurological issues such as Tremor and Seizure activity, loss of spacial-awareness, etc.
For example, did you know that ALL COIL/SPIRAL UVB BULBS, unless they are the newer, self-ballasted type (rare), regardless of the brand, the UVB output, the UVB strength, the wattage, etc., all emit extremely harmful light-rays that are a by-product of the manufacturing-process used to make them? The other issue is that even for Reptiles/Amphibians who actually REQUIRE a UVB light in order to be able to digest, absorb, and process the Vitamin D that they eat in their food, which in-turn allows them to absorb and use the Calcium they eat in their food, unless a Coil/Spiral UVB bulb is one of the newer, self-ballasted bulbs, none of them emit enough UVB light to do anythign at all for a Reptile/Amphibian unless #1) It's a 10.0 UVB-output and a T5-strength bulb, and only if it's totally unobstructed by anything, such as a mesh/screen lid, etc., (or glass/clear plastic, which blocks 100% of ALL UVB LIGHt, EVEN FROM THE SUN, and #2) The Coil/Spiral UVB bulb is withthin at least 12"-18" of the Reptile/Amphibian, which in-turn causes the serious health issue above...The same goes for all "Compact" UVB bulbs as far as being at all beneficial, they don't cause the health-issues that the Coil/Spiral UVB bulbs do, but are just way too weak to do anything (meaning UVB bulbs that are shaped/look like a regular lightbulb), unless they are the newer, self-ballasted Compact UVB-bulbs, OR they are a Mercury-Vapor Compact UVB-bulb (which emit strong UVB-light PLUS HEAT)
(UVB light actually only ACTIVATES the Vitamin D3 that is ingested in the food in most Reptiles, and Vitamin D3 is needed in all living creatures (basically) in order to be able to properly absorb Calcium that is ingested, that's the relationship between Vitamin D3 and UVB light, it doesn't produce Vitamin D of any kind, the creature must first always eat/ingest enough Vitamin D in their food first for UVB light to do anything at all for them, otherwise it does NOTHING)...
The bottom-line is that when it comes to birds/parrots, there is absoutely NO REASON to put any type of UVB-bulb over your pet bird, because if your pet-bird is deficient in either Vitamin D/D3 or Calcium, they won't get any from a UVB light or even from natural Sunlight, as UVB light DOES NOT PROVIDE VITAMIN D/D3 OR CALCIUM TO ANY LIVING CREATURE!!! Your bird must EAT/INGEST ALL of the Vitamin D/D3 and Calcium that they need/use!!! And birds are not at all like Reptiles/Amphibians who's bodies can ONLY use ANY of the Vitamin D/D3 or Calcium that they eat/ingest if they absorb enough UVB light each and every day, either 1-2 hours of natural Sunlight each day, or at least 10-12 hours of light from an artificial UVB-light if they are kept indoors (preferably they are under either a Mercury-Vapor Bulb or a UVB Tube-Light that is a 10.0 T5 UVB Tube-Light that is at least 18" long, and that is replaced at least once a year if a T5; if a much weaker 10.0 T8 UVB Tube-Light (or a T8 strength Coil/Spiral or Compact UVB light as well), then it must be replaced once every 6-months, as ALL T8 strength UVB lights stop emitting ANY UVB light AT ALL after 6 months of being on for at least 8-hour each day, even though the UVB lights will still turn-on and light-up.
Birds must get ALL of their Vitamin D/D3 from their food each day, and they must ingest enough Vitamin D/D3 in their food each day to be able to absorb the Calcium that they eat each day. However, unlike most Reptiles and Amphibians, birds DO NOT need UVB light in-order to be able to absorb or use the Vitamin D/D3 they eat in their food!!! That's where the disconnect is with most people, they either think/believe that #1) UVB light provides Vitamin D/D3 to living creatures, which is does not at all, and that #2) Birds require UVB light in order to use any of the Vitamin D/D3 and/or Calcium that they eat in their food, just like most Reptiles do...THEY DO NOT!!! And the risk that most-all artificial UVB lights presents to birds is enough to not even think about putting on over your bird!!! It's bad enough that around 90% of all UVB bulbs that are manufactured specifically FOR REPTILES/AMPHIBIANS WHO NEED THEM TO SURVIVE are either so weak that they provide little to no usable UVB light to Reptiles or they provide absolutley ZERO UVB light to Reptiles because even the screen-lid to their tank blocks 100% of the already too-weak UVB light, OR they are seriously dangerous to the Reptiles they are made for and commonly cause Blindness, Skin/Scale Damage, Skin Cancers, etc....That's bad enough...But our pet birds don't even need or benefit AT ALL from being under an artifical UVB light in the first place!!!
If you are worried about making sure that Remi is getting enough Vitamin D/D3, Calcium, Phosphorous, protein, amino-acids, or any other nutritional requirement to keep him healthy and happy, then you need to make sure that his regular, daily-diet is adequate and all-inclusive, and if he doesn't have an Avian Mineral-Block then absoutely get him one, because it will not only provide him with additional Vitamin D/D3 and tons of other essential nutrients, but it will also keep his beak nice a trim...But don't put him under any UVB light, it's not going to help him in any way, and could very likely hurt him, either pretty-directly or in the long-run...And the other thing that we ALL forget about most of the time, myself included, is that getting our pet birds OUTSIDE for NATURAL FRESH-AIR AND SUNSHINE is probably the second most-important thing that we can provide them to keep them healthy and happy, second only to a healthy daily-diet.