If I'm reading this right, the gear will fit on the basket but won't slide over the clutch shaft when you try to put the basket and gear back on the clutch? Some of the Horstmans I have had were set up for Limited Modified engines and had the back side of the drive hub cut down so the basket would go directly on the crankshaft and not attatch to the clutch like you normally would with a retaining clip. The driver's for those came with a small journal or something that would slide onto the crankshaft first, then you would put the basket on the crank over the journal, then your thrust washers and thrust bearing, then the clutch itself. The clutch bolt and key would be the only things holding the clutch and basket together when you tighten the clutch bolt. Not sure if this is what you have or not, its hard to see what you mean without pics.
Also, if you plan to keep and use the X5, I suggest getting an extra basket for each extra gear you have, they use Allen bolts to hold the gear to the basket as I'm sure you noticed, and once the clutch is used a couple times those Allen bolts get hard to get back out without stripping them out. Every X5 or Reaper clutch I had before I had to drill the bolts out just to swap drivers, and put new bolts back in it, sometimes it would ruin the threads in the driver if I wasn't real careful drilling the bolts out, thats why I started getting an extra basket for the gears instead trying to change gears. I tried using anti-seize, torching the bolts, everything I could think of and nothing worked, they always stripped out. If you can swap the horstman baskets and gears for a bully style basket and use bully gears, I highly suggest that, its alot cheaper and easier than buying extra baskets or new gears all the time, and alot quicker to change drivers. Dont think bully makes a basket small enough for the X5 but there are a couple other clutch builders that sell clutches that have a smaller basket like the X5, I believe Ward makes a revolution clutch that takes the same size basket except they use bully drivers, but not sure on that, been awhile since I had an X5.