Thousands of people applying for tourist visa extensions but hardly anyone applies for a DTV extension...read the reports on this group instead of trolling. The general advise by immigration is "do a border run".
What's your medical issue that you would be denied travel by plane? Anyway, go to Laos. The Cambodian and Burmese borders are closed (except for Mae Sai-Tachilek, which is open if you sign up for an expensive tour via a Burmese agency and get your visa through the Burmese embassy in Bangkok or the consulate-general in Chiang Mai).
Land is fine if you own a car...in many ways more exciting than flying, which is a form of public transportation. In any case, definitely stay out several days and return to Thailand using a different border crossing (I almost always do this).