I use cheers and I think it's more versatile.

- got your fire drill and I'm handling it... Cheers (don't worry about it)

- won your business, thank you so much... Cheers (celebrate)

- scheduled a meeting for next week. looking forward to talking to you... Cheers

To say thanks after everything seems odd to me. Kind of means nothing in many contexts.

Cheers at least reinforces your tone and personality (assuming that's how you are) in really any context and how you conduct business.

I still use thanks of course to be thankful, but almost always close with Cheers.

Where are you based? In the UK cheers acts a generic end of conversation, with connotations of friendliness and informality. I tend to use cheers over thanks when I want to imply a friendly/casual tone or when I've helped the other person out. In the latter case it functions the same as 'your welcome' but without requiring the other person to have said thanks first. Cheers communicates the same tone without the risk of coming off as passive aggressive.