Don't worry so much to collect every part you need all at once.
If you build it in modules you can collect parts for the 1st 5 modules and get them on the 1st baseplate, then get parts for the next 2 or 3 and add those etc
The timing and setup of this project is so fine that it may take a little while to get every module timed perfectly with the rest.
I find it kinda fun to browse BL and I always add parts that I feel I could use more of for other projects, I bought a few hundred of the common sizes of DBG bricks and loads of tiles, so when I build another Akiyuki machine I already have them.
I haven't already said it but many MANY thanks to Akiyuki for his incredible design and generosity, and of course theRebricker and Blakbird for their work to bring this project to fruition.