Making this journey at almost any other time of year would probably be totally wonderful and enjoyable. And I do understand you have work holidays to factor into your plans.

But, you should plan on relentless traffic for the period April 11 - 20, with crowds at every rest-stop and site between Bangkok and Chiang Mai. I assume you are familiar with what goes on during Songkhran so your vehicles will be unrecognizable after a day or two - a lot of people actually get their cars glazed in wax, not something I'd do personally, for protection during Songkhran. And I assume you understand that getting accommodation at this late stage may be challenging?

My advice would be to pick a closer, slightly less traveled destination or two. If you must travel many leave at off-peak times but this requires driving at night. Personally I always leave early, departing a few days before peak travel, say April 8 this year, and return on the first workday after the weekend following Songkhran.

Leaving on the 13th may not be all that better as you will run into festivities along the way.