You've done the most important thing - or say you're going to - by getting LPA in Health and Welfare, and Finance.
Failure to do this, esp the former, and at a later date the State - comprised of Social Services, the local NHS CCG, pretty much anyone except you in fact - assumes control over your parent. It will be the decision maker, not you. And the State saves money from your parent's death, even if your parent is self-funding.
Order from Parkinson's UK the free Parkinson's handbook, and the Advanced Parkinson's handbook, also free, too. Check out the forum as well.
Personally we got nothing really of use from Surrey's Parkinson's Nurses, indeed one suspects they are glorified Social Workers who use the matter to get over the threshold and case the joint. Yours may be different, but beware that if you are in a county or local authority with a high elderly population, they may have ways of working through that backlog.
For some reason, Parkinson's seems to be treated differently to other illnesses, in a more ominous way. Maybe the medication is very costly, I don't know.
On the subject, the drugs can adversely affect one and you might think wrongly that it is the Parkinson's suddenly taking hold when in fact it's just the drugs that need tweaking, esp if they send the taker crazy batshit, seeing things that aren't there, getting paranoid and so on. It's just the drugs most likely, so address it. Watch out if they are also taking painkillers.
Do a bone density test. A stumble due to poor walking can easily lead to a fracture that goes unnoticed for two weeks then worsens because old people don't always notice the pain at first. Check for osteoporosis and if it's there then Adcal D3 and weekly Fosimax (sp) may be prescribed.
Two things: keep walking with a Zimmer if necessary, the use of steps has been shown to have a big neurological advantage.
Also: high fluid intake also can ward off mental erosion it seems, start with 300ml in the morning, aim for 1.5 litres daily, more in a heatwave.
Care homes are a racket, and often work in conjunction with a corrupt local authority to hush up any wrongdoing.