It takes A LOT of heat to soften cured epoxy. I recently removed a bunch of epoxy that was half glow poweder from one of my lights and even with direct contact to a 30W iron, it was very slow going. Even if you could get the heatsink hot enough, odds are the emitter might not survive. You have your own personal safety and skill level to consider too.
If it were me, and I had decided that maintaining the heatsink's original design was worth possibly sacrificing the emitter, then I'd put the heatsink in a vise and heat it with a plumber's torch, then pry up underneath the emitter with a jewler's screwdriver. After the emitter is off, I'd have to carefully remove all the epoxy left behind while trying not to damage the andozing which is necessary for electrical isolation where the emitter contacts or wires might touch the heatsink directly through the epoxy. I'd probably use the tip of my 30W iron for that part.
If I had decided that the emitter is more important than the heatsink, then I'd try to double up on the wires without removing the emitter from the heatsink by drilling new holes through the heatsink for the additional wires. With careful, deliberate work with a dremel, I'd have to remove any heatsink metal and wire insulation in the way to gain access to enough copper strand right near the emitter base to solder onto. Once the copper is exposed, I'd epoxy around it to insulate the new joint from the heatsink before soldering the new wires onto the old.
Honestly, I probably wouldn't bother with either option. They both have a very low chance of success.
I think you have one realistic option here.
What's done is done. Leave this one as is rather than risk destroying some pretty expensive parts. If it really bothers you, then build another one first. If you find that a direct comparison reveals such a difference that warrants risking destruction of the first one, then go back and try to remedy this one with one of the two options above. If your remedy fails, at least you haven't destroyed your only working version.