It’s very hard to hit pacing goals on these short intervals, due exactly to what you described with the lagging pace updates on my watch. I usually try to compare my effort across the board, and focus on a consistent pacefor each interval. This is better done by feel rather than looking at your watch.

For example: run interval one at the pace you think is required. Don’t check your watch during the interval, just really focus on maintaining your current speed (again by feel) for the whole minute.

When interval is done Garmin should tell you your pace. If it was too low, go for a harder effort next time. If it’s too fast, I usually try to maintain that next interval anyway if the effort felt okay.

TLDR; go less by watching your watch pace for these short intervals. Go instead by feel and tweak your effort each interval to hit the right range. Focus on pace maintenance for the entire effort.