Good question. Recovery activities definitely count as training time. Especially with the long durations that you’re talking about, the time should be included in your training log.
I would recommend trying to figure out how much of your alpine days are actually spent moving (versus breaks, belaying, etc) and then apply a multiple to the moving time as you’ve suggested.
Another option is to use something like Training Peaks which accounts for intensity in its training log calculations (although you’d still need to adjust for idle time).
I hope that helps.