Yes, that's right. Foreigner can add their name on the Thor.Ror.13 or so called "Yellow Book". However each amphoe asks the different papers to be submitted. Some amphoe is easy, some doesn't. Anyway you could give it a try if it is not too hassle.

To add on the opinion on the last answer:
The rent is still valid until the end of term. Because the rental agreement will not be terminated because of the transfer of ownership according to section 569 of Thai Civil and Commercial Code

I used to stay at Tanita Resort in Udon Thani when I traveled there. It was quite nice. There is a big lake, swimming pool, a private balcony hut adjacent to the lake. If I am not mistaken, I paid 1000 baht. The drawback is it is out of town.