I agree...I think a smooth, finer nib would show an immediate improvement in legibilty.
I had to re-read a couple of bits(especially the 7th word!), but think it presents a quite pleasant 'picture'; the lines and words are well-spaced and it has a look of 'maturity' about it.
Where speed is concerned, you don't need to connect all the letters in a word, but you should aim to keep your pen moving to the right as much as possible, even when it's off the paper.
There are some clever movements, like the way you sometimes join the i-dot with the top of the next letter.
However, something to try
not to do, IMO, is to lift-off, mid-word, at the end of a down-stroke and then have to re-start with a leftward movement at the top of the next letter...just think how far your pen has to travel!.... but rather turn upwards at the end of that down-stroke, before you lift-off, if you prefer to, or if the next letter requires it (if you see what I mean?). ...I'll try to do a quick & dirty scan to show....
An example might be the 't' in 'sometimes' at the r/h end of the 3rd line..... if you could turn it upwards at the bottom and start the following 'i' with a little upwards 'lead-in' stroke, I think that would save you a nano-second or two!
(see scan....sorry it's messy, just trying quickly to illustrate the point about connections...the green ink was on the scanner!)

(Handwriting adviser Kate Gladstone recommends dotting 'i's and crossing 't's as soon as you've written them ....IIRC...., but I feel more comfortable doing 'em all at the end of the word)
Just my thoughts...if you
can find some time to practise, I think I'd recommend you to concentrate on the 'invisible connections' I've mentioned, and just to work on making your vowels more legible.
That way you should, quite quickly, see an improvement in both speed and legibility.
I hope that's useful, and that Kate reads your post and gives her expert opinion....which mine isn't