Etymological connection between 戻る and 元

Question

It just crossed my mind that both 戻る and 元 sound really similar. The Japanese Wiktionary page on 戻る even lists its first definition as "元の場所に帰る". Consonants becoming voiced also seems to be common in Japanese, such as through the process of 連濁, so と becoming ど doesn't seem too far-fetched either. Since I don't have access to (or know of) a good etymology dictionary, I figured I could ask here if 戻る derives from 元.
(In before the connection between the two words is really obvious to every good speaker...)

Answer 1

My source here is the Nihon Kokugo Dai Jiten entry here at Kotobank, where the verb もどる is the fifth section down, starting with the line 〘自ラ五（四）〙 (「もとる（戻）」と同語源).

According to this, the verb is first cited to a text from roughly 1001 with an unvoiced middle consonant as もとる. I think this bolsters the idea that this is a verb derived from the noun もと (spelled variously in kanji as 元・下・基・素・本 etc.). The voiced もどる appears later, apparently in the 1200s or 1300s. My suspicion is that the bilabial nasal //m-// at the start of the word may have gradually caused voicing of the following //-t-// to result in voiced //-d-//. There may also have been a need to differentiate from homophonous verb 悖【もと】る with the same [もとる]{LHL} pitch pattern, but a different meaning ("to bend something, to warp something").