Hmm… I disagree about δὴν, which I think I pronounce with a circumflex, only I think I manage not to overdo it for once 
With πάρα, πόδων and ἄνθρωπους you’re probably right. I think the problem is, again, the stress accent on the first syllable in Finnish. Here, I do think I manage to get the pitch accent at the right place (or what do you think?), but at the same time, I’m unable to avoid stressing the first syllable. So we get words with two accents, one of pitch and one of stress! στεβόμενας is similar, except for some reason I stress the second syllable – I think the pitch is correct, no?
I have to repeat a short sentence like this 20 or 30 times before I’m even remotely satisfied, and then recording the file, converting it and uploading all take their time.
That sounds like a recipe for burnout. Maybe I can suggest the following: Since feedback from other people is more important than perfection in something that is meant to be an exercise, why not do 2-3 practice read throughs, and then do your recording. In your recording, imagine that I’m sitting there trying to write down what you’re saying (which I will be). Go slowly, because you know that I have trouble transcribing speech, and if you misspeak, just correct yourself. I’ll be able to catch the correction.
For me, the criticisms of off-the-cuff recordings are actually more useful, because I start to find out what my bad habits are. And if you worry that you will sound stupid, well, join the club.
The way I see it, the pitch accent makes sense only in the context of a longer utterance. So in my opinion, it’s a good idea to try to construct a whole sentence at a time, to try to see how the language might work in longer chunks. Since it’s difficult, it takes many, many repeats before getting it even remotely right. But it’s much more profitable to try to do it really as well as possible, at least a couple of times, especially as we don’t have native speakers to correct us.
I know I should go slower, but that’s just something I’ve never learnt to do, unless I really, really concentrate, not even in my own language… It’s a speech defect of some sort, if you know how to fix it, tell me!
It’s easier with poetry.