We started packing as soon as we were sale agreed (process is quicker here - about 6 weeks from sale agreed to moving). It was our first house and we were there 30 months, so not enough time to really accumulate loads. And it still took us most of that time, doing a box a day and putting aside the spare bedroom to fill with boxes.
Now, looking at the clutter, even with a storage unit available (we have 1), unless you can dedicate a number of hours every evening after work (like, 3-4 hours at least, DAILY), and preferably move at least some boxes, hobby items etc to the storage ahead of time (that can be part of the 3-4 hours), you won't have any time for things other than moving on the 2 weekends.
DH and I packed up our house but got movers for the boxes/furniture. I have also moved a DUncle (who is a serial mover for reasons of his profession) on a number of occasions - he also usually gets professionals for the transport and a lot of the packing too, but there is a lot to organise and that needs to be done personally. He did the last 2 moves without professionals though, just family and friends using cars and a hired van.
DBro also moved using family last year and a rented van.
And I am also used to packing up the van for my Cubs going camping every year.
Don't underestimate the amount of thinking in loading the van itself so everything is fitted securely and won't move in transit (both for your safety and to prevent damage to your stuff), and to make sure each load is as full as possible to reduce trips and that it is not top heavy or otherwise dangerously loaded.
And the amount of energy that moving boxes in and out of vans, onto trollies and stacked into storage, and again back out of storage into the new house - is also astonishing. You will start out great, but literally hit a wall (and need hot tea/cold coke and sugary biscuits to keep going) as the day progresses. But there will still be a mountain yet to be done.
I really would start moving as much as possible to the storage unit now, at least a car load a day, and spend a couple of hours daily packing up the less used spaces - attic, cellar, out of season clothing, spare bedding you won't need for a couple of weeks, art from the walls, book cases/music collections (keep out a few to enjoy while you work and for your "collapse in a heap" time) etc. And get into higher intensity of packing the more everyday spaces and items closer to completion day - but aiming to be fully packed up the night before so you only have to strip beds, load up, clean and go in the morning once the paperwork is done. Cos you will need to keep lots of energy for your arrival in the new place also.