Your Drs reluctance to prescribe a new Pap machine may be due to restrictions from his employer (for example an HMO), but if that is not the case, AND your DR has determined that using a Pap machine is not detrimental to your health (first do no harm) then there is no reason for his reluctance. In any event, unless you acquire a new machine from a non-approved source, you WILL need a Drs prescription.
The rub here is: Will insurance cover any part of your purchase?
Many insurance companies will not cover the purchase/rental, if you have a AHI less than 15. However, if you have comorbidities that threshold drops to 5 AHI. Your BMI likely places you at the 5 AHI threshold group.
Bottom line is that you will need a Drs prescription, unless you purchase on the "grey market". If you current Dr is unwilling to prescribe, and you are adamant, you may need to find another Dr.
An alternate plan (to obtain a Rx) might be to sign up with a on-line service (like sleepmedrx.com) and begin with a home sleep study that includes a their Dr consultation and potential Rx.