Have you tried a soldering iron ( or pyrography pen - essentially a variable heat soldering option ? The product specification guide says it can be “ sealed with a hot blade “.
I have a peter child system which uses wire tips but you can get solid tips which may work better in this situation. Either way you want a VARIABLE HEAT tip or you will damage the material .
[URL unfurl="true"]https://www.turners-retreat.co.uk/pyrography[/URL]