Can I enter Thailand on a 30-day exemption and then use my 60-day visa after a trip to Kuala Lumpur?

No,you can't officially choose to enter on a 30 days visa exempt if you have a valid 60 days tourist visa. But you can always leave Thailand and come back on a 30 days visa exempt. Then extend it another 30 days at the local immigration office.

I would not count on that. The immigration officer might use the visa already in your passport.

But you can extend your tourist visa by 30 days in Thailand anyway.

You cannot choose to not use a visa that has already been issued. You can politely ask but we've never received a report of anyone being allowed to not use their visa to enter Thailand. In fact we've received multiple reports of people that tried to not hand the printed visa over with their passport, but the immigration officer saw it in the system and forced them to use it to enter.

So you should expect that you'll be required to use your visa to enter Thailand. You have the option to apply for a re-entry permit before you leave which will keep your 60 day entry stamp alive when you leave. This means when you return you'll be stamped in on that stamp instead of a new 30 day visa exempt stamp. The end date will remain the same as when you left and the days will continue ticking while you're outside of the country though. You will not get any "extra" days by using this method.

I've read the IO might make you use the Visa when you first arrive in Country. I'd wait for verification from one of the normals when the've woken up 😊

Yes if it is still within the 90 days.