To remove the needle jet first remove the slide assembly.  Then remove the main jet and main jet washer (you do have a main jet washer, correct).  Then use a soft punch and lightly drive out the needle jet.

Keep in mind that the needle jet has an orientation pin in the carb body.  When you replace the needle jet, the slot in the jet must align with the pin.

Is your replacement a genuine Suzuki part?  Is your existing needle jet brass or stainless steel?  Please post picture when you get it out.

Thanks Mike.

The main jet has a brass washer.
The existing and replacement parts are brass. The replacement just came in a rebuild kit. The one on the bike now is the original.

There was also an alignment spacer fitted to the top of the needle. It was a brown plastic. Is that needed ? As it is brittle and broken.

Wow!  Moarpower that is a lot of info.  I think you are changing too many things all at once.  For now, I suggest you stick with my suggestion to change the spark plug, remove the air filter, and run it.  Then let us know what happened.

"I used my existing jets and needle jet and needle until today when I used the replacement needle to adjust the clip height. I added a taper to the new needle. "

How exactly did you add that taper?  Where on the needle did you start the taper?  Do you have measurements of your taper?  Can you post a sketch?  What sort of measuring instrument did you use?

This is a sketch of a modified stock needle.  Note that the needle is plotted out in increments (20mm, 30mm, 40mm, 45mm, 50mm, tip).  The modified taper starts at 45mm and runs to the tip.  The diameters are given in one ten-thousandth of an inch.  That's four decimal places.  If you don't have a micrometer with a vernier, you can ruin the needle in a heartbeat.

Did your WOT problem start when you installed the modified slide needle?  If so, maybe you put too much taper on that needle.

"I used my existing jets and needle jet and needle until today when I used the replacement needle to adjust the clip height."

Did it run lousy at WOT with all the existing jets and slide needle, or did the WOT problem start after you replaced jets & needle?

"There was also an alignment spacer fitted to the top of the needle. It was a brown plastic. Is that needed ? As it is brittle and broken."

That plastic spacer is critical to proper performance.  When you remove the spacer, it sets the slide needle 3mm higher than the factory setting.  In the world of slide needles, that's a lot.  If you are running a needle with multiple clip grooves, and you place the clip in the bottom groove, and then you install the needle without the plastic spacer, the needle is now probably about 5mm higher (richer) than the factory setting.  And then, if that needle has an extra taper sanded on, you are adding a phenominal amount of fuel at WOT.  Sounds familiar.

I'm having trouble following all your changes.  Did you/are you running a three-groove needle with the clip in the bottom groove and a modified taper and no spacer?

This is a picture of the stock configuration.  The stack from top down is:

Plastic Spacer

e-Clip

Washer

Spring

Is that how you are setting up your slide needle?

Are you making sure the slide orifice holes are not covered up by the needle retainer plate?  The plate can be installed upside down.  It will obstruct the orifice holes.  When it is installed correctly the holes will be fully open.  Like this.