Since he's already sore even in shoes I'd be tempted to try him barefoot, but only with an experienced trimmer because you are likely to need lots of advice on treating infection and boots and pads, conditioning etc to improve the feet. Boots and pads can do a very good job of keeping them comfortable so it might not be too bad. Some horses even turn out to be less sore once the shoes are off so well worth a try.
I've seen cr*p TB feet turn into nice feet barefoot, its a great way to improve the feet even if you do want to go back to shoes longer term.
You can soak in borax even with shoes on so might be worth trying even if you don't want to go barefoot. What I've found with mine is that even without soaking at all (one unhandled horsie with minging feet and one tempremental baggage that didn't like getting wet persuaded me to try not soaking) well trimmed feet, no shoes, the right diet (its worth trying magnesium and reducing the amount of sugary stuff even with TBs) and hard ground gets rid of any hoof wall infection pretty quickly, but if you can't get everything right straight away then soaking with something to kill off as much infection as possible at least keeps it under control a bit. Soaking every day is excessive IMO, I wouldn't do more than a couple of times a week.