Google reCaptcha v3 timeout problem

Hi Ray, I know this is above and beyond the call of duty, but you're the only person I can think to ask for help!

I've integrated reCaptcha v3 into a client's multiple websites which have contact forms using Universal Email on a number of pages, so the contact form and email script are in shared PHP files and embedded on the pages. Everything seemed to be working OK, however the client has reported a number of people saying they've submitted the contact form and didn't get a response. I check the database log and sure enough, these emails hadn't been received, but others had.

After doing some digging and by a process of elimination, I've discovered that the problem is caused by the reCaptcha's default timeout setting of (I think) a couple of minutes. So, if someone takes longer than this to type in the message, the email doesn't send. However, to them it looks as if it has because the page redirects to ?sent=true and the success message appears.

I've spent hours this morning trying various 'solutions' I've found both on the Google Developers site and on Stack Overflow, but can't get any of them to correctly override the timeout. Is this something you could help me with? I can give you links to the solutions I've found and I think I just need to find the correct way of integrating it into my code without breaking anything. Happy to pay for a dedicated support session as I need to get it sorted out urgently!