Can I reasonably compensate myself as Power of Attorney for my Mother?

Legally and ethically, NO. Legally you can not amend the POA document, only your mother can. Wouldn't we all like to change our employment contracts as we take on more responsibility?
If your mother's assets are great enough that you are left with an inheritance then your sister will be free to gift you with some of her share at that time in acknowledgement of your extra work.

I've often seen information on this site about personal care contracts where the caregiver is compensated for daily care of the parent. Personally, I've never seen compensation for POA/Health care guidance. One option might be for the non POA siblings to kick in a bit of their inheritance when your Mom passes. My out of state sister used to send me gift certificates for a massage or restaurant as a gesture of her appreciation for all I did for our Mom.
Can you pay yourself? I guess it depends upon whether or not you think your Mom will eventually need Medicaid and how far out that option is. It also depends upon how the POA document is written. I'd say that chances are it wouldn't be appropriate.

No. You can't pay yourself out of POA or estate legally.
You can document all hours, travel, etc and keep diary of time. Talk to other sibs or those who have interest in estate and let them know you are doing this. Decide on reasonable hourly compensation for this. Get sibs agreement -- maybe a legal agreement.
You will have to rely on faith as to whether or not the sib or others will honor and relinquish a share back to u in the end.

My brother has agreed, but he often reminds me that it is my choice to visit and help or spend time with mom and he chooses not to....therefore, he may not want to give me my share in the end. I'll have to accept that.

I would have thought the time expended would have been greater before your mother was in a care facility. As others have stated, you have no right to change or amend a document created by your mother. That would be fraud in my opinion.

And your sister has no right to suggest a change or payment either. She's not the proxy who granted the authority.

Further, any attempt to receive payment now after your mother has been diagnosed with Alzheimers could appear to be exploitation, under the theory that if your mother wanted to pay you, she could have made arrangements when she had an attorney draft the POA.

There's another option and that's to try to consolidate and minimize the time you spend on her care. Bill management isn't that time consuming; shopping can be consolidated once you know what is provided at the facility; just buy more when you shop.

Home maintenance can definitely be time consuming. Are you contracting out these chores? Is there any consideration of selling the house and using the money to pay for your mother's care? Or is Medicaid a potential future concern?

I think you should see an attorney on this for clarifications as to your specific legal position.
"Most of the details of what you can and cannot do will be addressed in the power of attorney document itself."
Start there.
" You are almost always bound by basic fiduciary duties, which will essentially exculpate you for actions taken in good faith and in accordance with your fiduciary duties to act in the best interests of the principal. You'll generally not be protected from fraud, gross negligence, or willful misconduct."
So that still leaves you in a vulnerable position because you might think paying yourself $10 an hour to sit with mom is better than paying $20 an hour to a non family member. But a sibling might say, mom doesn't need a sitter. So if you had proof that mom needs a sitter then maybe you could protect yourself and pay yourself and fall under the area where you are looking out for the best interests of your mom.
"Also important here would be the documents in place for the care you provided. Was there a care contract? The more documentation the better."
We live in a litigious society. The same family member who won't spend an hour to visit mom will make it their life's mission to condemn your actions and yes, possibly sue you. So can you pay yourself as POA, not according to you in that you indicated your POA doesn't say so but you might be able to reimburse yourself for funds spent on behalf of mom and those funds were for a specific task that is above reproach. If you are spending too much time doing home maintenance hire a property manager. It will cost more but would be within the bounds of what you are legally allowed to do and free up some of your time and keep you away from fraud and all the other problems.
There are also personal shoppers and delivery services. Just saying.
Sometimes following the letter of the law doesn't seem practical or in the best interest of the principal but can keep you within the bounds of the agreement unless it is determined to be one of the areas where "you generally will not be protected from fraud, gross negligence, or willful misconduct."
See an attorney to go over your particular paperwork and list of heirs and moms assets so you can do what is both legal and feasible for your situation. You will want an attorney with knowledge of the Medicaid laws for your state.

I'm just repeating what has been correctly stated. To receive payment for POA duties it would have had to be written into the POA document to legally allow that to happen. The only legal round about at this point would be to file for guardianship and then negotiate for payment. If you apply for guardianship and are awarded - the entire cost of doing so can be paid from your mothers funds.

I was once a caregiver for a cousin who passed and held durable POA, I offer this as a life experience. Keep good records of everything. Their expenses are in your care. No one is expendable or invincible and all that is done for the person is lost without careful records. Yes, bill them because as things decline, your role will change in the eyes of the person you are trying to help. After 3 years of providing shopping, maintaining appointments, housekeeping and laundry, I risked my full-time job because I was seen as a willing volunteer by the beneficiary cousins who never once offered support. I was not compensated.