I am basically the same proportions as you and another poster on here. My trousers are shortened to at least 29 and my waist is a 39. I just have a short and stocky build. I do have extra weight at this point, but at best I can slim down to a 34 waist or so and I would look quite thin.
I started wearing braces a little less than a year ago. I was tired of belts. The trousers sink down to below my gut, the belt buckle then digs into my stomach and I become uncomfortable. All I can think about is wearing a stupid belt and how it's uncomfortable for me. So, I just stopped one day. I bought braces and had buttons sewn in all my trousers. I was getting a new wardrobe to start a new job at the time anyway. I never went back. I have literally worn a belt one day where I have worn trousers in that time span.
Here are my tips:
1. This is the most important - be confident. Don't be afraid to wear braces because they're different. It's ridiculous that people think they're funny or out of place. They hold your pants up well. I don't wear them for style. I wear them for utilitarian purposes. I don't usually want them to be noticeable but if they are oh well. If you go on being confident in yourself people are likely to think they're cool or just not say anything. I think you're very unlikely to draw negative attention to yourself with them.
2. I try to blend mine in with what I'm wearing. I don't wear loud braces. I have some plain ones and I have some with vertical stripes. I think gray and tan or brown are great colors. I don't have burgundy yet but I think that would be a really nice color too.
3. I do hide mine for meeting with clients or walking around in public. I'm an attorney so I wear a jacket to meet with clients. I wear sweaters with a tie underneath quite often around the office or to and from the office as well. This would probably be a similarly good look for you. I've gotten compliments on it lately.
4. I think it's ok to walk around the office without a jacket and since I wear braces 100% of the time, my coworkers do see them. Nobody cares. They compliment them, if anything.
5. I don't abide by the rule that you aren't to wear braces with trousers that have belt loops. I do this all the time. The belt loops are a fact of life on the pants I wear, in general. I wear the braces to keep my pants up and they do that really well. Nobody would know the pants have belt loops if you were wearing a jacket or sweater.
6. I try to match the leather ends to my shoes but I don't always. Due to limited selection, I can't always make this happen. It doesn't look bad to me, per se, when I can't match them.
7. Albert Thurston makes really nice braces. You should check them out when you're ready to buy a serious pair. They are pricey.