Connections in a Flow that runs on List item creation

[Chad_V_Kealey]

I'm creating a request process using a SharePoint list with a customized (PowerApps) form and using Flow to both log each step of the process to a list and perform a series Approval on each request. Here's the basic process:

1. User submits request
   
   1. Flow Creates item in Log list
   2. Flow Emails requestor a "Submission Received" message
   3. Flow starts first stage approval
2. First stage approver acts on request
   1. If denied, email requestor and end flow
   2. If approved, email requestor and start Second stage approval
3. Second stage approver acts on request
   1. If denied, email requestor and end flow
   2. If approved, email requestor and end flow

All of the emails are using the "Outlook Office 365 Send Email" action which (apparently) is tied to my mailbox/account. All of the emails being sent are from me, which is not ideal. Likewise, when the log entries are created, they are created by me (which isn't really a problem, but if they could be created by the requestor, that would be better). 

So, is it possible to set a flow that runs on SharePoint list item creation to use the connections of the person creating the item, rather than the author of the flow? It seems like adding people as "Run only users" might do it, but that apparently is not an option for a Flow with the "when an item is created" trigger.

Please don't ask me to share screenshots of the flow....it's massive, so I'd need a dozen or more just to show it all.

Also, in testing with my team, I found that users needed to have "Contribute" permission to the original list in order to open the PowerApps form. I'd prefer they have "Add Only" permissions (a custom permissions level that doesn't allow them to edit the item after creating it), but if that's not an option, I can work around it.

[#2]

We have created a Generic Account named after out Intranet that we create Flows under.  This way it sends emails from that account and not our personal accounts.  

[#3]

That's a valid approach in some situations, but would not work for us. We have dozens of sites with these kinds of processes and the departments that own them will (most likely) not want to pay for additional licenses for service accounts. 

Really, what we need is a way to manage the properties or permissions on connections in Flow. Basically, for each connection, there should be a way to set whether it should use the credentials/permissions of the Flow Author or the Flow Initiator.