From what you post above, I think there’s a pretty good chance that will fix you up. I’ve had to replace the clutch master cylinder on my Corolla a couple of times over the years for similar reasons. On my Corolla what happens when the symptom first starts to rear its ugly head, it will shift normally most of the time. But if I come to a stop sign or stop light and while waiting I keep my foot held down on the clutch for 15-30 seconds or so, while in neutral, waiting to shift to first. Then when I try to shift to first, a lot of grinding or usually it just won’t move to first at all. To get it to go to first I have to pump the clutch pedal two or three times, then it will go into first like normal.
Replacing the clutch MC is a bit of a technical challenge on the Corolla, b/c of where it is located, right in an inaccessible corner of the engine compartment on the firewall. I have to loosen the bolts holding the power booster and shift it to the side to free up some room. Then there’s the problem with loosing & tightening the fluid fittings. A normal wrench just won’t fit into the space. It’s like the most wrench unfriendly spot in the car … lol … I need some kind of short bent wrench for that job, but I don’t have one bent enough or short enough I guess. I finally figured out a way to do it with really – I mean really – long pliers with 45 degree angle bent tips.