Salutations Nick,
While I have no visibility into the email teams quota procedure I can speak to my experience with quote increases in general. Quotas generally don't get approved for new apps, this is particularly true for the occasional email quota request I have submitted on behalf of customers. This is to prevent spammers and other abusers from flooding the system. Generally for email providers blacklists are created based off of IP's. So if someone gets one of the Google IP's blacklisted it causes issues for hundreds of apps.
The reason we ask for APP ID's is a way to confirm identity and see which projects you need quotas for. I cannot say exactly why you were asked for the billing app ids (as I stated I have no visibility into the email quota process) but I would have asked something similar in case you wanted to show an app with high traffic that your email isn't associated with. Our ability to 'browse' apps is limited to protect your information and privacy. We don't just randomly search for apps and look at them. Each time we touch any information on an app we need justification (ie customer said we can look at this app because they are related).
Quotas are applied on an app by app basis. You have 75 apps, we would need to get approval from other teams for each app independently before processing it. We generally don't apply quotas account wide (ie manually go to each app and apply the quota) unless there is specific justification for it.
As I started earlier quota approvals take time because they involve many safety checks and approvals from multiple teams. This is all done to protect everyone from spammers and abusers. As you said you submitted for multiple apps so we need to get each one approved by each team to proceed.
I would recommended (as I do with customers I work with regularly) looking at
SendGrid. While it is a third party tool you can start with '25,000 free emails per month'.
As I stated a couple times I have no visibility into the email quota team, but I can try and get an update for you. If you PM me with the 5 apps you applied for quota increases I will try and contact someone from the team. I cannot guarantee I will get an answer but I will do all that I can.