Is it permissible to leave what remains of reading the Mushaf before completing it and start anew with the intention of finishing it on one of the odd nights to benefit from the great reward, while continuing to read without stopping?

If the intention is to leave the remainder of the current recitation (khatma) and begin another recitation to complete it on a specific night, such as Laylat al-Qadr, then this is permissible. The recommended method for completing a recitation among the Salaf was to finish the current one first, and then begin another.