I see. AWS ACM also provides free, extremely easy to use wildcard certificates, provided you use the right parts of their stack (CloudFront or ELB or CloudFormation or Elastic Beanstalk, etc).
For a pure Let’s Encrypt solution I’ve seen a few questions on here that ask the same thing as you, but I’ve yet to see any out of the box solutions.
I vaguely documented an approach I’ve used to distribute certificates previously, but it is very DIY. I don’t see any reason why wildcards would affect it.
Also not sure why you have committed to wildcards if you only have 7 names. Letting each endpoint (as in, load balanced virtual host) issue a single certificate for whatever names it needs, unless you actually use the *. label, seems more secure (principle of least privilege) and less operationally complex.