Hang on though.
If you can change gear with the engine off, then it's more likely a clutch problem.
I presume that when the gears get stuck you pump the pedal and that doesn't make any difference... Then switching the engine off allows you to change gear (select neutral). and it's fine for a while until it gets moody again?
If you had a moody master cylinder, then pumping the pedal would get some kind of reaction... and it would do exactly the same moodiness as soon as you started driving the car again. It doesn't know it has to be moody just sometimes and not others.
On the other hand, if your clutch pressure plate fingers are falling to bits, the release bearing can jam. Releasing it (with an engine off and putting it in neutral) gives it a chance to re-seat itself and if you're lucky it ends up on "good" pressure plate fingers, and it works again until it jams again.
How many miles has your clutch done? 500 clutches seem to fail from around 50,000 miles.. (town car = lots of gear changes) although 60k is more typical and some fellas can run them to 80k..
It's rarely the friction plate that wears out. Either the pressure plate fingers wear (worst case is that they start falling out of the bottom of your clutch bell-housing) *or* the release bearing wears out. Some clutch kits only come with the 2 plates.. and a garage in a rush/plucky amateur will not replace the release bearing if one is not supplied in the new clutch kit box. So... 90% it's your clutch, not the master cylinder.
If I'm unlucky.. then the master cylinder is easy to replace.
If it was me, I would replace the whole assembly including the Quick-Detach connector at the end. If you separated the connection joint when you fitted the slave, it should come undone (you "lift" the nylon collar and pull it apart.. easier off the car).
If you never fitted the QD connected to the slave, (just the slave using the old pipe and leaving the old QD connector untouched) you should still have it (new and shiny) so fit it now.
If the clutch still jams afterwards... *I told you it's the clutch*
Ralf S.