You’re doing a great job. A couple of hints (I’ve hand fed several tiels and a bazillion finches) .... thickening the formula was brilliant and clearly is working, if his poops seem to become dry though or his skin becomes shiny and pink, he’s dehydrated. At that point work in one runnier serving per day.
If he is hungry, feed him. The only time this is not applicable is if he just ate in the last half hour. As long as the crop empties thoroughly once every 24 hours, you’re good. They sometimes have little growth spurts and want to eat every 90 minutes. That’s fine, let him eat. If his problem was malnutrition from the earlier food or from the only-4-hours feedings, he’ll have to catch up.
In his little nest, if you put shredded clean paper and mash out a circle for him to sit in (like a bird nest) that will help with the splay legs. They often develop from having too much room/no substrate. BUT....see below....
Little ones like this have often developed improperly, something that happens in the egg or even due to missing or diseased inner parts. Hence, splay legs and not growing, maybe. That’s why the vet wanted to put him down. So please know that despite your best efforts he could die and it is not your fault if that happens.Totally out of your control.
Thank you for giving him a chance. I know how hard it is to feed a baby around the clock.