I have a couple of those trays, but it is something i keep meaning to get more of, now that i'm branching out (i keep one tray, victa fine pars, such as deco clips and cowl screws, the other is larger bolts and mounting nuts, etc, then i have one of the old style metal units with all the little compartmental draws, which separates my carby parts, and a another larger draw unit for carby bodies) as i only have enough for the victa parts.
That bit about the screws may come in handy, some of my sockets are a little worn too!
I have a stack of old milk crates for things like cowls and starter, that i can see straight into, and a long steel box for old engines.
i have a few other crates, which i think i may well label, as i cant see into those ones.
I think i might grab that de-greaser this week, i tend to be OK doing the old victa's using old fuel and a brush, but i am finding the more complex engines need a little more to get cleaned up well, and i really hate trying to negotiate a dirty engine, apart from the mess transferring you mentioned, its also a bugger trying to keep muck out of the delicate parts!