@qoba x 3: I'd say that's how slow you want to start IFF you're sure you're having issues. Generally go a bit slower than you really need to, 1-3 or so times, in those cases. Then alternate native-average-speed attempts whenever detail work get's boring, with slow-speaking native speed most of the time otherwise.
My key is (as a pro-pro-pro-level linguist) to repeat at six full times full-speed, once I get it perfect (with the native speaker standing there, I feel the pressure ;-] ... a HIGH FI audio recording or better video-with-stereo is OK too) making sure I don't trip up(catching breath is OK) at all, even if this means restarting the count often, even twice or so, if I need too, or even four times if I'm very new to the language/lect.
Only way to improve the trick that I know of is: Always keep going across a couple of word boundaries, even before the start of your "etude" even if that means you need to add something of your own up in front (the last chunks added) to do so. Especially in Frenches of France or the Carribean.
Never learn grammar wrong, always play around and talk to yourselves, and stay interested in real phrases and accents AND obscurely over-erudite pre-modern written-only pomposities.
Always have toggling between fastest/fastish for yourself (potentially pretty damn slow, relative to anybody but an "announcerish emphatic declamatory" language-lab example) ultra-perfect-pronunciation "textbook" attempts (speed one), and best attempt at fast Native or favorite-native(s') idiosyncratic flavor-exact mimicry in your arsenal, so whichever gets boring, you can switch to the other for half a minute before quitting, so you can end on a good note.
Thank you all. If someone would translate this or @qoba's answer into (France std) French, I'd love to hear how to do so, and learn whether or not I'm using the wrong language (lost the linc to the FAQ).