First, I'm not a pro.
The toilet flange is supposed to be on TOP of the finished floor. You've gotten away with it, but if there ever was a leak, the crud would now be going inbetween your flooring levels, and you might not know it until it had been happening for a long time.
I'm not sure whether you can stack that many flange extenders together, but I'm pretty sure I've seen flange bolts long enough to work. Many of them come extra long with notches so you can break them off easily (well, moderately) to the proper length.
I don't know how your flange is attached and what type of pipe you have or what access you might have. But, with this many layers, and the flange that far below the surface, you should consider raising the flange to the new floor height. Not sure what an inspector would say, it might not pass.