Stephen R Jones wrote:

....snip....

With the blackberries, I had thought about using a syringe to inject the
stems with glyphosate, but had no idea how viable this would be or what the
mixture ratio would be if I did that. So any further tips you or anyone
could give me would be greatly appreciated.

Wait for a warm day.
Cut stem.
Paint root with glyco straight and dip top in little container.
Repeat root application as stem sucks in glyco.

Well, that works for trees {:-) like privet.

Warm day means sap is running.
You want to feed stuff into root to kill it.
Same for top part as a cutting buried can shoot.

Apart from the thorns (thick leather gloves), I've found blackberry
reasonable easy to pull out. It just that the roots have a lot of other
stuff around to snag you.