Incorporate logo in Figma Weave

Hi all! I’m trying to create an image in Weave: a flip phone lying in snow, with my company's logo displayed on the phone's screen. I have a reference photo of the composition of the shot and my png logo. When I use those as inputs to the image generate node (I’m using Flux 2 Pro), it re-draws my logo and messes it up in various ways (wrong spacing, font, all kinds of extrapolations). I don’t want to use a Compositor to insert the logo because 1) the phone is tilted on an angle and it looks obvious that the logo is just slapped on top and 2) I want it to have a glowy/glitchy effect like it’s actually being shown on the flip phone. 

Any advice on a good workflow to seamlessly work the logo into the scene while preserving its shape for brand consistency? Or are there any image generator models within Weave that you’ve had success interpreting it?