Well, I don't. The verb to attend comes from the Latin, meaning “to stretch to.” From this developed the meaning “to direct the mind or energy to,” and later “to direct one's care to.” The meaning “to present oneself at a meeting” is dated back to the 17th century.
The suffix -ee is given four meanings in the Shorter Oxford Dictionary and is admittedly a muddy area. However, none of the meanings comes near to denoting the subject of a verb (the person who does the thing, such as attending a meeting). It is I who attends the meeting, and not the meeting which attends me. The nearest legitimate use listed would be in the adoption into English of the past participle of certain reflexive verbs in French, such as “se refugier” (to remove oneself from a place in the interests of one's safety), which results in the word refugee. While I have taken refuge from meetings at times, I have never thought of attending a meeting as a reflexive activity. Perhaps “attendee” should be reserved for those who attend meetings in order to listen to themselves.
I may have occasionally been the smallest person at a meeting and might therefore qualify for the diminutive suffix, rather as a small coat becomes a coatee, but, since I was never an attend, even being small would not make me an attendee.
There are already two words for a person who attends, and they are attendant and attender. Curiously the Shorter Oxford Dictionary gives the former the meaning at issue, whereas I find the second the easier to use. But surely there is no need for a third.
My suggestion is that we learn to accept, when talking about what we do, that we probably haven't invented a new practice and so we probably don't need a new word.