If you can heat the copper up to just barely glowing red, you can use silver brazing (aka “hard soldering” — 80 percent silver or higher) and have boiling water handy — as soon as you’ve removed the heat the silver braze hardens; then drop the metal into the boiling water. The excess flux explodes off the surfaces rather than sticking tenaciously. I’ve used that with outdoor sculptures made of copper, brass, and bronze. You get a better contact that doesn’t tend to fail, which won’t matter for heatsinks — but you also get much less corrosion on the surfaces, which might matter.
Also, you can then use lower temperature solder to attach things with no worry about disassembling the base.