Hi Stephen,
To migrate mailboxes from on-premise Exchange Server to Office365, you can consider cutover migration or staged migration. Here are some articles for your reference:
Cutover migration: technet.microsoft.com/.../jj874016(v=exchg.150).aspx
Staged migration: technet.microsoft.com/.../jj874018(v=exchg.150).aspx
Besides, as you said, if you want to talk with our engineers, you can submit a service request. For detailed information about this support channel, please see: office.microsoft.com/.../contact-support-for-technical-presales-billing-and-subscription-issues-HA103836042.aspx
Thanks,
Young Yang