If you’re not afraid of some Tasker hacking, you could use Tasker to make an HTTP request to your public profile, and then parse out how many meals have been entered for the day. Here’s a Reddit thread where someone described how they queried their MyFitnessPal profile, though I don’t think they were sending the data to Beeminder, and I think they were querying different data than what you want (calories, protein, sugar count in their case). I could help you with the Beeminder part though.
This is the URL they were using for their own profile. It seems to default to showing today’s data. Change the date range to 2016-02-23 through 2017-02-23 to get some sample data to look at.