Hi jazzbiker,
My oldest /slowest PC (Dell mini 10, has 8+ years old?) has already 1GB RAM. So my "studies" for minimum RAM for a small/rescue linux (not necesary tinycore) were focused on virtual machines (VM). The pristine (virginity) boot state of pseudo-HDD is not a concern for VM, so goal was to use less RAM for guest, from main host RAM.
TC is wonderfull for 64+ MB RAM. For 32Mb up to 64MB RAM the number of applications are VERY limited in scope (for me). Maybe something like DSL (damn small linux) is more suitable. For basic/primitive things (partitioning, formating, text edit, audio, even basic network) I am still looking at Kolibri linux, with 8 MB RAM demand
or wonders like
http://www.toms.net/rb/ for less than 4 MB RAM.
About busybox: as long as just someone call a busybox applet (like grep, from /init script?), then all busybox code loads in RAM (and stays in RAM as long as there is still free RAM) and give speed to other busybox-applets (like you later call the mount applet), without more RAM consumption.
My aproach thinking was a little slow speed but less RAM consumption. Load "mount" or "grep" when/if I need them (not so often).
You see, one size does not fit all cases. But for very low RAM, exceptional methods are summoned.