Yes I think we are talking about the same hose. Mine came with a 13 inch hose. It was very small for me and kept dangling behind my back. Every time I had to inflate or deflate the BCD I had to reach behind my back and grab the hose. It was too short to hang in front of my shoulder. I also have wider than average shoulder which makes it more difficult to reach the 13 inch inflator behind me. It feels like you are trying to scratch your own back and cant reach the itch spot (know what I mean?)
As for me dumping the weight, I don't remember if the tank was full but yes that could be a possiblity. I remember after busting my BCD having to struggle just a bit to stay neutral at 16 feet. Every time I exhaled I would start to sink. Then, I remember debating whether to drop the weight. Once safety stop was done, I dropped the weight and just regular breathing caused me to ascend gradually. Once at the surface I did not have problems swimming to the boat. I think your analysis is correct that the tank had enough air in it to cause the negative buoyancy effect. Not too much but I do remember sinking slowly from the safety stop every time I exhaled. I wish my memory served me better though.