I am thinking, that when ionised, electron pressure only holds electrons away but does not prevent nuclear collisions because they are unbounded to electrons. But when not ionised, atoms are being pused together with electron repulsion holding back the nucleus.

I also doubt if the furnace is cold and high pressure, overcoming electron degeneracy pressure causes inverse beta decay and turns the thing into a neutron star? Then you wouldn't get new elements but a pile of neutrons?

In stars, nuclear reactions happen at high temperatures and pressure and at death stage of a massive star(becoming a neutron star), all the electron degeneracy pressure is overcame by gravity and the same inverse beta decay happens and protons and electrons combine to give massive pile of neutrons.

If you think of a bunch of solid atoms(low temp) put in high pressure, why would nucleus react anyway? Nucleus are bound by electrons and are not able to collide with other nucleus in that state. Electrons need to combine into the nucleus with high pressure. For the case of hot plasma, nucleus are able to move through the electrons and react. You don't need to overcome electron degeneracy pressure for that.

(I think i said things that i earlier said i'm not sure about, but this is a bit more thoughtful response while others were sent in a hurry mind)