It's difficult to say, because we all have different Parkinson's symptoms what will work for one person might not work for another.
However, I found that running solo definitely didn't help me improve, it was too easy to give up on a run. The thing that really improved my times was in races, mainly the 5K parkrun with a few other 5K races thrown, plus some 10K races as well. My 5K PB is 22:41.
It took me a long time to build up to 10K but once I had built up my stamina to last the distance I only started to improve my times when I started entering races earlier this year. I've managed to get my PB down each race. It is only 50:52, so I'm not going to win any prizes but just being able to take part is prize enough.
Entering a race makes you take it a little more seriously than a training run, you build up to it during the week to 'peak' on race day at the weekend. The competitor in me then takes over and I automatically run at a faster pace. The incentive is always there to catch the person in front. Occassionally the fear of finishing last can spur me on also, when in a higher quality race.
Training with my local running club also helps. It brings an element of competition into it. It also provides mutual support and encouragement.
I see you have done a lot of running over the years. That inevitably leads to wear and tear on various parts of the body which can slow you down as time passes, not to mention old age and Parkinson's!! I have only been seriously active since my diagnosis (I did a lot of hill walking but I don't think it caused too much wear and tear) so consequently I haven't worn out any parts of my body yet which I think is why I am relatively injury free and don't feel any little 'niggles' which can affect performance.
Don't let Parkinson's hold you back, fight it.