other field types (i.e. time)

Yes. You can add more field types yourself using the new API that we’ve added since Types 0.9.4. Have a look here for an example (at the bottom of the post):
https://wp-types.com/2012/01/types-0-9-4-adds-cf-group-display-per-templates-field-api-and-bug-fixes/

And, don’t forget to show your love. Go back to the project page, rate Types and indicate that it’s working for you:
https://www.ads-software.com/extend/plugins/types/

Fab, this looks great. I assume I add this to my theme’s functions.php file? Is there any documentation on this? I’ll have a play but I’d love to be able to add a couple of time fields. Would also be great if there was a forum where people could share their examples. I tend to learn by seeing other people’s examples.

There’s some documentation on the first few lines of that PHP file. Yes, the right place to add it is in the theme’s functions.php.