If he had followed our written plan (plus the deep stops and oxygen window stops) instead of the computer, he would have done relatively short shallow stops and been out of the water 20 minutes sooner--to what effect?????
So the short story here is that he made a safe dive, you made a safe dive and nobody got bent.
The complication is that you were not able to stay together in a group during the ascent. This increases risk, especially, in your case, to the diver who was left twisting in the wind by himself with an ever decreasing air supply.
And THAT is the reason that technical divers need to not only square off in terms of gasses but also procedures.
Years ago I used to dive with someone who was a strong believer in RGBM. I was using Buhlmann. After some initial problems with alignment like you described, we finally settled on doing his deep ascent (notice I am not saying deep stops) and then my shallow stops from the point at which his ceiling caught up with mine. It resulted in longer dives than either algorithm would have prescribed alone but both of us were able to dive the algorithm that made us feel most comfortable and we were able to stay together during the ascent, which we believed was important.
These days I still dive a different algorithm than my buddy. He dives with a Petrel on Buhlmann with 30/70 and has a Suunto RGBM-like thing as a back up. On nitrox dives, I dive an old Vytec, from before Suunto started bubble-wrapping their Buhlmann.... The main difference is the ceiling. My computer and the Petrel calculate within a minute or two the same TOTAL deco obligation (which is the only number I need/want to know, hence the old Vytec). That's not strange, it's pretty much the same algorithm. His computer often picks a deeper line from about 15 metres and up because of the GF-lo while mine is very persistent is keeping the ceiling around 3 to 4 metres until you are at least 30 minutes over the NDL.
In the course of many many dives I've developed an ascent strategy based on input that I got from, among others, some people online, like Steve Lewis. The idea of all the "deep stops" we do is to limit the ascent speed, and amazingly by just slowing down the ascent to 3m per minute from the 18 metre stop and onward, his "deep stops" usually clear before we get there and the difference to the dive only shows up at 9 metres. We are usually back at 18m for the gas switch before the hour is up so the controlling tissue from the Buhlmann algorithm isn't saturated yet. This stop is usually extended in order to do gas changes because we're almost always free-hanging in a 3m bubble of green at this point and we need to be accurate about depth.
We often make a particular dive that involves 30 odd minutes of deco so I know that if I ascend like this and put in a 4 minute stop at 9m that we can then ascend to 6 and finish our deco based upon the respective eccentricities of our computers without extending the dive any more than about 4 minutes.
So yeah, you can align two different algorithms or even an algorithm and an ascent strategy (as I do) without it affecting the total deco very much. The point is to make the right choices and for the right reasons.
R..