First of all, I always try to ensure neither me nor my clients are not re-inventing anything. Any business should be spending money only if necessary. Also, the business should be a win-win. So, before I start detailing about my bid, I would like to check with you on whether you have checked the following Chrome extension?
Inbox Pause by Boomerang
Disclaimer: I am in no way connected to Boomerang.
In my opinion, it has all the options you want. ex. If you click on the "Pause" button, you will get a popup window where you can configure when you want the emails to be delivered.
If you are happy with the "Inbox Pause by Boomerang", then we may not need to develop this project. We might work sometime in future, if you have some other project and my expertise suits your needs.
If you have checked that extension and feel that it is not solving the purpose you want, then please read my bid below.
I have extensive experience in developing browser extensions and also with Gmail.
I can confidently say I know what exactly is required to develop what you are asking for. I have worked on similar requirements in the past. I have been working in building Chrome extensions since 2012. I have extensive working experience with Gmail APIs since 2014.