Talon, I’d hold on to that gi. Yes a gi is a modern garment. Yes a gi can be recognized for what it is. Yes you should invest in a good tunic ASAP. However, a gi is way better than a t shirt or tank top. A gi under a vest or tabard, as Magnus suggested will work and a gi top on its own has elements and lines that can work well if you dress it up right.
The thing about the gi is that you need to break up that silhouette that makes it instantly recognizable as a karate uniform. If your gi has long sleeves, you can wrap fabric around the forearms to make the sleeves more form fitting. Forearm armor such as vambraces or bazubands also work great for this. If your gi has short sleeves, you can simply wrap your forearms, or armor them. Lower on the body, you can wrap your lower legs in fabric, or wear greaves. Then blouse the pants around the knee. A good belt is a solid idea- I think using your sash around the waist will just enhance the ‘dojo’ look. You can use your sash as a baldric. On your feet, you will need to stay away from obvious modern colors and designs or you’ll blow the illusion.
I’ve been there dude. My first big event was Gates of Fire two years ago and I had to pull out a gi. Black, short sleeves and worn out as hell and I had to accessorize big time. (I had garb, but it was all courtly, delicate stuff. My gi is what I wear instead of a gambeson under my heavy kit) I did not want be that guy who ruined the youtube video. From a javelin throw away it was passable but you can bet that at Badon the same year I had a fighting tunic ready.
You can probably tell by my ‘fix your gi’ list that there is no real shortcut to getting a decent set of garb. Garb is just one facet of the LARP thing that you have to address. One way or another, whether you are trying to pimp up something you already own or are starting from period patterns, you have to put effort into your look. In a way, it shows your fellow players that you care about their Dag experience. As soon as you can, I’d get a comfortable, rugged fighting tunic. They’re not expensive and if you have to make one, not too hard to make. You can keep your gi as a backup or a loaner, or as a set to wear under whatever armor you wind up putting together.