Both of my parents have been in a nursing home with dementia for almost 4 years. I handle all of their financial affairs and do have power of attorney. They qualified for Medicaid soon after their move to the NH. Their Social Security benefits are automatically deposited into their checking account each month and I insure that their balance never exceeds $4,000.
My mom had her SS & retirement direct deposited into a checking account of which I was a signature on. Checking account was also done a POD to me as I was executor as per her will & envisioned the $ left would go towards whatever after death costs. Mom went into a NH & onto medicaid & was there about 3 years. What was an unexpected plus in keeping account active was that moms checking became the estate account for when probate was opened, so there was a clear history of all finances from when she as alive to beyond death.
Every month I wrote out a check to the NH to the penny for her required copay or SOC (share of cost). The PNA ( personal needs allowance) remained in her checking so her account built by $60 each month. It was nice in that when I came in I could do a bigger buying restock for her, or take her to see her old hairdresser & pay by check. You do have to make sure any month ends under 2k in the account as the Medicaid recertification may require you as DPOA to submit maybe the last 4 ms of bank statements & if over 2k poses eligibility issues. I did set up a personal trust account at the NH for her to use for beauty shoppe and the on site "canteen". Kept about $200 in it & her 2nd NH send a statement of the account every 90 days. For both NH my mom was in, access to the trust account was done at business office during the week and for 1 before noon - which could or could not work for you (you sign a ledger & have to be an authorized signature on the account). When mom died, the trust account $ balance was sent to me & deposited into the old checking account which now was the estate account.
If you could be doing probate, having an account to roll into for probate will make all easier.
NH, well I've found will press family to make them the payee. But it is NOT required. Should you decide to move mom to another facility, getting the rep payee changed will be most difficult. I moved my mom from her first NH to her second and eons better NH within her first year. It would have been quite a battle if NH 1 had been rep payee.
You may be asked to personally sign off a financial responsibility contract. You do not have to do this. Just sign whatever as " Jane jones smith as DPOA for mary jones". & get a copy of every age on all peoerwork. But if you are late in paying, the late fee is your expense. My mom got paid on 3rd of the mo & copay due to NH by 7th, so no issue. But if yours get paid a Wednesday later on in the month, it could pose late fees.
Personally I think the rep payee is a process encouraged to be found to be "needed" as it provides work for SSA employees. It can't be automated or done by bot like most other SSA functions can be.
Also, when you say you are making sure their account never exceeds $4000, what are you doing with the excess, if any? Where is it going?