How can I get models (attendees) to take me more seriously as a photographer with a small camera?
There’s a famous phrase: “clipboard mentality”. In the 1990s, projectors started to become more common in colleges. Thieves would walk into a room, holding a clipboard, and steal the expensive projection equipment. While class was in session. Until this problem became notably widespread and security was forced to crack down on the issue, people just trusted professionally dressed people who looked like they had equipment and seemed to be doing good things.
“I have a clipboard. Therefore I’m a professional and expert, and know what I’m talking about.”
How this applies to you is: equipment matters. Even if you’re more skilled and can come up with higher quality results in smaller equipment, people’s perceptions may not take all that into account, so the equipment you use can matter. So, let’s not pretend like it doesn’t.
A bunch of what I’m about to say may involve some trade-offs between usability and practicality (including ease of transporting things), and feasibility may vary based on just where you are. Naturally, use creativity to customize (slightly, or extremely massively) based on what you think will effectively work and what you desire. Just don’t think that you should limit yourself to only your small camera, and you may be able to come up with something.
Often they carry tripods and reflector screens as well.
So you’ve offered your own solution. If successful people are getting the results you desire, and they are using that technique, then you using that same technique may help. That is one approach that doesn’t involve you needing to change camera equipment.
Even if they have giant tripods that you don’t want, consider some sort of small thing which at least shows that you’re able to stabilize your equipment. Even if you don’t use that equipment, just having it available may lead to them taking you more seriously.
Note that the equipment doesn’t need to be professional photographic gear. You mentioned using a T-Shirt.
If you can corner off a section of land, make that area yours. Take some rope and make a “tunnel” for people to walk through, and shoot them at the end. Maybe have a prop, even if that isn’t anything more than a bar stool people could sit (or stand!) on. Then people may pose for you because using the prop just looks fun.
Having a portfolio may also be helpful. (Ensure the participants look happy. Then your potential participants will be more inclined to want to do the happy-making thing.) remco’s answer suggested a tablet. That may be one approach. Another approach may be to have a bunch of print-outs in a strip which you can hang on a wall (or toss half over a fence). Or somehow incorporate that into your costume. The back side of your shirt/jacket/whatever can be advertising space (whether you write something fun, witty, or just show a photo), possibly helping to serve you with your next customers while you’re active with the first one.
A bit of music may also perform wonders. (Probably preferably wordless, so that you don’t feel any need to talk over lyrics.)