Hey!
Congratulations on the AC invite!!
I completely get why you are worried about how it might look, but I don't think asking to be considered for the direct TC would come across badly as long as you approach it in the right way. Firms are generally very conscious that candidates apply to lots of different firms and that VS dates can clash, and I'd say it is a pretty common situation. It is quite common to hear people ask to be moved to the DTC application process, and whilst it'll be firm dependant, I've definitely heard about people that have had some luck with it!
I would just ensure that you frame it positively and show that you remain genuinely interested in the firm. For example, you could explain that they are one of your top choices, and you'd really value the opportunity to be assessed for their training contract, but unfortunately you already have a VS that you have committed to and the dates overlap. Following that, you can ask whether it would be possible to be considered for the direct TC route instead.
If anything, I'd say it shows you are being proactive rather than just declining the opportunity altogether. At the end of the day, you don't know unless you ask, so you might as well double check whether it is a possibility!
I totally get that it might seem like a long shot if they recruit mainly from the vacation scheme, but there's absolutely no reason why you can't be a part of the DTC offer holders, and most firms will offer at least a few TCs through the direct route. When I applied to
Reed Smith through their direct training contract process last year, I genuinely had very little hope that it would result in an offer - just goes to show that you never know!
I definitely wouldn't let the fear of "looking bad" stop you from asking - this is a very reasonable request (that I'm sure they get quite often!), and you are clearly a strong candidate if you have secured another VS already. I hope you are able to sort something with the firm, and best of luck with your upcoming VS!