Generally, I have always (35 years) felt that having the pipe in tension helps, and even contractors that have said that their particular tool does not require it have requested 10% overpull at the wellsite - this includes plasma-cutters.
Anecdotally I have heard that if pipe is in compression then with a plasma-cutter the pipe can re-weld. Seems plausible, perhaps.
I have seen good results from the Owen Split-Shot. Fired in the connection it splits the box and allows you to pull out without actually needing to make a complete cut.
The other most common reason that I have seen for a "failure to cut" is actually attempting to cut where the pipe is not actually free. I have seen this happen where use of a free-point survey was dismissed and not run, or it was run but then ignored ( "but we need to cut deeper for the side-track" )
Sorry to hear you are not having great success with your cutting operations, have you considered using a tailored Explosive Jet Cutter.
I have attached a brochure for your reference.
The MCR plasma technology is reliable, however when there are issues it has been found to be job planning and job set up that have been the main issues. Not knowing the specifics of the job the questions/point I would have/make are:
Was the plasma cutter positively anchored during the cut? If not was the pipe perforated prior to making the cut? If none of these options were utilised you would most likely get movement of the cutter during the cutting phase. If this happens you will not cut the pipe.
Another point to consider is that the cutters have to be centralised to make an effective cut. Was the tool string well centralised - you have to make sure that the tool string does not naturally "bow" and cause the cutter be become de-centralised. In some cases when this happens you may get a partial cut, if this is the case then you should/may be able to circulate.
Lastly are you sure you have cut at the top most free point, I have seen many cases where a free point log has been conducted on only a small part of the stuck tool string where they are assuming they are stuck free and do not log any higher. If they had they would have encountered a higher stuck point.
Hope this helps any questions please give me a shout.
Welltec have a e-line mechanical cutter which uses grinding pads rather than cutting blade. Able to cut in compression (tested up to 30klb) without jamming. Leaves a clean cut (top and bottom faces) so no subsequent dressing run required, and creates very fine swarf (powder).
It's also able to cut several times per run. Recently performed a 5" drillpipe recovery op where 23 cuts carried out, including 1 run with 7 cuts. Drillpipe had been cemented in over 500m so was cut in 20m sections to subsequently wash over. Deviation was >80deg; cutter was run on Well Tractor. Can be run standalone: anchors itself in ID.
Daft question, fixed installation or floater? With the mechanical cutter I could imagine slippage if you've got a bit of heave (depending on how you're compensating the rig up but with stuck pipe I'd imagine you could still be seeing half the heave downhole?)
Plasma - did you run an anchor? If unrestrained it is possible to slip up hole just as you initiate the cut (as the cutter pushes you up the hole leading to a mis-run) you can waste the charge cutting a track/groove up the pipe rather than getting the clean cut. If you did run one, can the eLine provider confirm the anchor held firm during the cuts on Plasma? Possible to increase the restraining force? Run a stronger anchor / with toolstring lying on the lowside is it holding as planned.
I've had a fair degree of success with the Spex 3-3/8" RCT (clean cut)... http://www.spex-innovation.com/spex-offshore/cutting-solutions/non-explosive-tools/
An ugly option for fishing (but potential dependant on your next step) is getting a severing tool in the hole, I have had good success when unable to apply tension (offline abandoments and prepping tubing for recovery), but not good if you need to get back onto the fish.
Another thought is centralization, how's the toolstring sitting in the hole (assuming cut depth is somewhere building up to your 69 degrees), plasma cutter would require centralization that may have been minimised to help get the toolstring down at that inclination?
Depth control - it couldn't be something daft like cutting on a tooljoint? (I struggle with that, even saying it, with 4 runs even if no correlation performed!).
Apologies if this is a much too simplistic response! Good luck.