(First, I know and haven't overlooked that this proposal will involve work from the good folks at SE.)
As much as I realize there's Beta sites spawning in all directions, the blue beta design is not particularly appealing. For instance Aviation SE and Engineering SE both look fairly dull in blue.
From this question on the Aviation Meta, it's pretty clear that perhaps one of the primary motivations for wanting to graduate is the site-specific design.
As a relatively simple (yet what I think would be time/effort-efficient) process would be to slightly enhance the banner on the Beta sites.
Add the site icon to the banner. Add a big wrench next to 'Engineering SE', and an aircraft next to 'Aviation SE' headers. We have this in the icon on the site list, so why not in the banner?
The more labour intensive (and rewarding version) would be to have a more elaborate banner design that sticks to the blue colour scheme, like the Meta site.
- The banner is visible on every page. It's almost the first thing people see.
- While SE users might be familiar with this 'Beta' concept, it's not clear
Aviation betais to outside people. What is
betain aviation sense? Adding a icon makes it a bit more clear and credible.
Adding a site-specific banner may help to give the site a nicer feel and boost credibility. This is particularly important to new visitors who are needed to enhance the user base (perhaps particularly so on less frequented beta sites). Ultimately, this would hopefully encourage more activity at earlier stages, leading to a quicker progression towards graduation requirements.