Can I extend my Thai visa exemption by 30 days upon arrival at Suvarnabhumi?

You could apply for a visa now. Come into Thailand on a visa exempt, stay 30 days, fly to Malaysia for the week. When you return your visa should be ready, that's almost 6 weeks from now.

Don't extend, you don't have time to deal with the visa struggle. just fly out to Malaysia after 30 days and come back after a week in Malaysia.

Unfortunately they are still giving 30 days visa exempt…at least as of Monday

Apply for a 60 days touristvisa which can be extended 30 days at a immigration office, then no need to travel out of Thailand for the 90 day period.

Since many embassies proces the application by departuredate, rather than date of applying, it could be possibel to get the touristvisa before departure, which will make the trip much easier and simpler.

In Bangkok you apply up to 45 days in advance, so immediately with visa exempt.

Unfortunately for you June 29th is the weekend so you cannot apply in Bangkok. You will not be able to apply at Koh Samui until the last week of your stay as they only accept tourist extensions when you have 7 days or less left on your stamp. Koh Tao does not have an immigration office.

You're going to need to figure something out if you like returning to Koh Samui in your final week or going to another province and applying, since you cannot do it before you go to Koh Tao.