...I am still convinced that balancing a rig according to the GUE definition is impossible...
I believe that when you do the calculation, it is meant to show you that if you are using a wetsuit for "deeper" dives; a wetsuit with a steel tank or especially steel doubles, that you will not be diving a balanced rig. People are frequently surprised by those numbers in the class. It is a gentle way to help people come to the realization that a drysuit or AL doubles, etc., might be a better idea.
From that, comes the discussion of how you achieve a balanced rig or mitigate that imbalance.
What you do with that moving forward is up to you. People have done Fundies with a wetsuit and steel tank, and even a wetsuit and steel doubles.
I'm not sure if the numbers are entirely correct either. The first time I used a HP steel 80 cf tank with a wetsuit, I emptied the wing when I got to the bottom at 80 feet, and had no issues whatsoever initiating an ascent. By the time I ascended a few feet, the momentum started and I had to vent gas as usual.
If you're concerned, you can make sure you can swim your rig up - with caution - for peace of mind. The only thing my GUE instructors told me was that it might have been dangerous to test it from 80 feet, and that 40 feet would have been enough. I'm not sure if they thought I swam it up all the way. I only continued until I had to start deflating, then continued the dive.
...the definition for balanced rig I'm using says "nearly empty tanks for the last stop".
But in practice both you and
@jadairiii are right - a simple recreational dive with a single AL80 seems possible as long as 1) you're perfectly weighted for the end of the dive with ~1000 PSI at 10ft and 2) you use very conservative gas planning.
If you're "perfectly weighted" at the end of the dive at the last stop, 10 feet, with 1000 psi, you will be *underweighted* if the crap hits the fan and you have less gas than that at the end. It will be more difficult to hold the stop, especially if you are task loaded.
The GUE definition of weighting yourself to hold the last stop with nearly empty tanks and making a controlled ascent to the surface is exactly right.
It might take purposely practicing with a tank that is getting lower to see how well you're holding a 10 foot stop. You can also reach back and feel if your wing is empty or ask a buddy. If you have much gas in the wing with a nearly empty tank at 10 feet, you might be overweighted or not venting fully.
Hope that helps...