I can understand your dilemma. I'm in the same boat and got the Eversheds PFO this afternoon as well. As frustrating as it is, there really isn't much that can be done. I prefer to look at it this way - what if there were a couple of spots open for the Direct TC. At least now, it doesn't hurt that much knowing the firm rejected you rather than you choosing not to apply and then regretting later when a spot could've potentially opened up. That spot could've been for any of us, who knows 🤷♂️
As for vac schemes colliding with a full-time job, I don't think it's that bad a situation after all. For one, your gaining experience. Secondly, I've often heard people finding it difficult to decide on making VS/TC applications based on their experiences. You could be a bit strategic here and apply for VS to firms that recruit solely/a major portion of their future trainees from vacation schemes and also make Direct TC applications to firms with a sizeable Direct TC intake. That way, your mitigating the risk of losing out on any opportunities.
If you happen to get a VS at a firm that recruits solely/majority of it's trainees from the VS cohort, then it's not a bad option to quit your full-time job. I know it's a risky option but if you prepare well and give it your best shot, no reason why you can't convert that VS into a TC. On the other hand, if you get accepted into a firm directly for a TC, that's fantastic. You have your dream job and you don't have to quit your current job too! You can certainly reserve a day or two off for interviews or ACs, provided you haven't used up all your allotted holidays 😄
I hope this helps and gives you some clarity. All the best!