... and yes, you're only required to have a 3rd class medical to instruct. 119.1(e)(1) excludes it from being a "commercial operation"
I asked an inspector once about this, and she said that they now interpret flight instruction as "educational services" not flight services.
/me shrugs
only problem with keeping a third class while instructing is if something else cool pops up along the way that requires a second class you're outta luck.