You can connect FastMail to gmail and never look at gmail. Your employer may not approve if you hillary your emails like that though, but that's what I did at a previous employer where this wasn't an issue.
I like your usage of Hillary as a verb. I don't understand the affinity against Gmail though. With the fastmail forwarding service are you still not using Gmail spam service and have Gmail access to your email anyways (not that I'd believe they do unless wearing a tinfoil hat)
I just don't care much for gmail's UI; that's all there's to it. And having all email in one place is more convenient for me regardless – saves having to open/check another service.
You're still using gmail's spam checking; it just uses the API (or IMAP? I forgot) to sync the emails to FastMail.
Have you considered setting up a rule using the Snooze feature[0]? Using this it should be possible to delay all incoming work email until a time that is suitable for you.
Edit: If you want your work emails to arrive only during work hours and otherwise delay them, you can use a Sieve condition in your email rule similar to this:
