As a layman, I think this would be excellent. I always love it when folks like Dennis Venema put unvarnished chunks of genetic code in their blog posts so you can look at the actual differences between various species. (Of course, I realize it's not quite "unvarnished" in the sense that Dennis had to know how to line up the relevant portions of the genetic code in order for us to easily compare them, so we got to see them neatly lined up like a problem set for homework, rather than as one might find them "in the wild," as it were. What I mean is that I get to see A/C/T/Gs in strings instead of just someone's interpretation of the data.) How much cooler would it be if we felt like we had unmediated access to the data to "see for ourselves."
Would it change minds? I think so. Sure, the Scriptural issues have to be addressed, and usually they have to be addressed first. At the same time, there's this idea you alluded to that evolutionary biologists just expect people to trust that they know what they're talking about, and people aren't willing to do that. But if you're able to say, "Don't take my word for it; see for yourself!" it's more welcoming and I think you'll get people wading into the data and finding that there isn't some big conspiracy to pull the wool over their eyes.
I think the trick would be making it user-friendly. I've seen in a few different fields, sometimes there are programs that are incredibly powerful and open-source, but you have to take a course or a seminar or a long series of tutorials in order to be able to use them properly. Ideally this would instead be something that would be virtually self-explanatory (if possible). I second James's suggestion about color-coding things and marking retroviruses, etc. Never having looked at a full genome myself, I would imagine that during the development of the software, someone would probably have to put a lot of hours into lining up two different genomes so that they could be compared (this human chromosome goes with that orangutan chromosome, etc.) and then highlighting points of interest so people could find their way around ("this is the GULO pseudogene over here," etc.). Otherwise, I can only imagine it would be quite overwhelming to wade into millions and millions of base pairs without a guide. That would have the opposite of the desired effect.
All the best in this. Sounds really promising. I hope you'll let us know how the presentation is received.
[Edit: for clarity]