I just went through this myself. A JT4 can be a MoFo PIA to say the least. I had 2 that needed to be removed from 18Ns, one MT5, and an MT3.
1) Tried wedges and home made press collars with abject failures.
2) Drilled holes in both check backs, proceeded to break or otherwise damage everything I had that would fit. Used penetrating oil over night, no good. Made a very tight fit "piston" rod and filled hole with oil, hoping to use hydraulic effect, no good...
3) On the JT5, it has a large lip. On advice from someone on one of the boards, I took 2 hardened pins and fit in the gaps, clamped it in the vise so it bears on the pins only, tighten down, and then whack the drift. That got the MT5 out, but no shoulder on the MT3...
4) Cursed, stomped, and glared at it. Still wouldn't move. Heated in case it was put in with Lock-Tite, and repeated all steps, still no joy...
5) Cut off MT3 and drilled out the center into the back of the chuck using my mill. Then chucked into my lathe to bore out the JT4 taper. It still wouldn't budge until I got it small enough to literally peal it out...
Later someone mentioned I could have cross drilled the MT3 and put a cross pin through to use the pin technique that got out the MT5.
There went a Saturday I'll never get back. Should have thrown the damn 18N in the garbage, bought a brand new one from the highest priced source I could find, and had it over-nighted to my door. Would have been way ahead...