Holding the cap iron in the vice with the work area well clear of the jaws, play a medium flame of a plumbers butane torch UNDER the work for about 30 seconds until the flux bubbles, then the solder is seen to melt. Do NOT use an acetylene torch or you will overheat it - you are aiming for slightly hotter than the average soldering iron.
Nudge the solder pieces towards the joint and run in a little more solder. Make sure the piece does not move outside the marks. You may find that the adjuster slot is 11mm wide - same width as the new piece - so you can easily see if the piece moves sideways by looking for light on one side or the other showing through.

Allow to cool naturally, then file off the extra solder, which may be considerable if you over-did the solder feed.

Try the blade for fit. If you find the blade is no longer central with the cap iron, the piece must have moved! Simply remove the blade, remount the cap iron in the vice, reapply a little flux, then reheat until the piece can be nudged into position with a screwdriver or similar tool.

NOW we have to recut the slot, Begin by drilling from the FRONT with a drill slightly narrower than the slot - in my case 4.5mm. Drill a hole at each end of the slot.

Then turn over and join up the holes with two hack-saw cuts which are just INSIDE the hole diameter size.

Using a small flat warding file (usually a couple of quid for a pack of six from your local "chinese tat" import shop) file the new pieces square with the face, until they line up with the old slot. Remember the old slot is only slightly too big - a matter of the dimensions of a gnat's manhood. So by making the new slot the same width but nearer the frog, it should be slightly too small where the Y-lever gets fatter (I hope you understand what I mean because I can't get a camera in there!)