I don't think you're crazy and I understand how you feel, but here is what I would do:
I would pack my "essentials" - everything you need for either your current or upcoming WIP's. Pack for yourself, the one machine and the tools and supplies that you *need* to do those things. Then put them in your car. (Unless your stash, tools and supplies are minimal enough for it all to fit in your car, then I'd pack it all and haul it all myself).
I don't know how your moving company works, but I used to work for one. We could not load anything into the truck that we had not packed ourselves. For two reasons: First being to save your butt - your stuff is not covered if you pack it. The second reason was to save OURS. If you have packed something that the company cannot move, for whatever reason (aerosols were a big one for us), and they don't know...and it causes any kind of accident/incident, it is not covered for us or you. Even for those rubber maid storage bins, we had to go through *every.single.item* in them before clearing them for loading (imagine the day I found a whole rubbermaid bin full of Play Girl magazines and HAD to go through it...)
I would rather have to re-fold and re-organize than lose it all with no reimbursement.