Frozen prize pile in canasta when all but one player has only 1 card in hand?
Your thinking is correct. If you are the only player who has more than 1 card in hand, then there is nothing to stop you from melding the rest of the cards in the draw pile. This has happened to me in a 2 player game (when playing draw 1 instead of draw 2). Nothing here would be different about 3 players. Your opponents have no way of ever legally picking up the discard pile or going out as long as your first discard after picking up the discard pile is a wild card.

You most likely should have been able to play out that hand and won the game. Being thousands of points behind wouldn't have mattered; you likely could have gotten enough points on that one hand to win.