The transition from sleep to wakefulness is literally a mode switch in your brain, and information doesn't disappear because you forget - it's because neurochemistry changes. The moment you wake up, completely different systems activate than during sleep, and old memories get pushed to the periphery, so to speak. This happens in minutes, but not instantly - you genuinely do have a window of opportunity.
What really helps: don't capture the dream as a full narrative right away. First, explore it visually. Stay in bed, close your eyes, and mentally walk through the details - places, faces, colors, sensations. Only then start recording. When you're rushing to tell the dream out loud, your brain switches to speech and logic mode, and the working memory of the dream itself shuts down. But if you let it solidify first through quiet recollection, then when you do record, you'll actually be pulling up details that have already stuck.
A minute or two of stillness and silence before recording isn't wasted time - it's an investment. The fact that new details pop up half an hour later is normal; associations work with a delay. But the bulk of the information you could've saved gets saved in those first five minutes after waking, as long as you don't panic.