Having taken one of these apart, converted it to 9 speed and then back again I might be able to help.
Take a 4mm hex key and a square driver bit (robertson #2 might just do it). With the top lid off put the hex key in the bolt in the middle of the spool and the square bit in the bottom receptacle and make sure they’re not loose. Don’t try to tighten them too much as the metal on the bottom is actually cheddar cheese and it’ll just round off.
If that’s not the problem make sure the spiral spring is sat under the discreetly clipped edge towards the middle of the spool (make sure you’ve got the shifter in the highest gear position to reduce tension and make it easier).
Lastly and you’ve almost certainly checked this, the plate screw has to sit centrally over the cover before it’ll screw in. Score marks round the outside of the hole will give it away if that’s not flush when you’ve been trying to screw it down.
I have a picture of mine with the lid off if it’s any use in comparison with yours to check all the springs are located correctly etc, let me know if you’d like to have a butcher’s.