Soda blasting seems to get nothing but positive reviews. I found that powerwashing removed a great deal of the heavier stuff although it was messy and the clean up a pain, but doable. After the powerwashing I used Interlux Interstrip 299E which is does not have the toxic methylene chloride in it and worked fairly well. The advantage to this and other strippers is that they have a gel consistency to them and you layer them on to a depth which keeps the solvent from flashing off and in contact with the paint. A plastic scraper works nicely for removing the paint after treating. At about $90 a gallon and I'd guess you could use somewhere between 3-5, it might make the soda blasting contractor look more reasonable.
The barrier coat should be fine with the Interstrip. You've already used MEK on it which will remove just about anything but a woman's grudge and isn't the healthiest product to be around. The trouble with the MEK is the same as acetone only less so; you cannot get enough contact time to penetrate and dissolve the paint before it evaporates. So you're basically scrubbing the paint off with a little bit of help from the solvent. Get's old quick, no?
If you're going to keep this a do it yourself project I'd try the pressure washer for the heavy stuff, giving due regard to laying out plastic sheathing for containment and clean-up afterwards. Then use the stripper for the remaining coats. I have not used the older methyl chloride strippers and cannot speak to their safety or effectiveness, although I have a sneaking suspicion that they are far more effective than the new and safer products.
“Scientists are people who build the Brooklyn Bridge and then buy it.”
Wm. F. Buckley, Jr.