Without an actual example to examine I can only guess how your large audio file was handled, but my guess is the "grey rectangular box" was an image file with a link to the actual audio file stored shared from a streaming server. There are different ways that can be done using HTML, or javascript that would "play" in most email clients. The object size would be pretty small and the audio content could be relatively large but that would not be noticed unless you were on a cellular network.
The simplest way of sharing your three hour meeting, I can think of, would be to copy the file to iCloud (if you have an Apple ID you have an iCloud account whether you know or use it or not) then control click on the file on iCloud and select Share from the context menu. You can then share the file to anyone with the URL, or only those you invite. Then send the url to your intended recipients in an email.
By-the-way since your file is of a meeting if you reduce the audio to monaural and the old AM radio bandwidth of 800Hz to 8 KHz I suspect the audio file size could be reduced by as much as 50 to 75% without significant loss of comprehension. It would not be ideal for a symphonic orchestra concert but more than adequate for the spoken word.
