Bug#46533: newer version of syslinux apparently fixes the problem
Well Juan was exactly right - as he suggested I just made a slink rescue
floppy with syslinux 1.43-1 and the Dell 90 Mhz box likes this one. I made
sure to use the standard-issue slink "linux" and "root.bin" images. I did
specify "syslinux -s" (safe option). Haven't tested with "unsafe".
The changelog for syslinux says 1.43 changes a delay parameter. I notice
that bootup from this floppy is noticeably louder, but it does work.
I haven't yet had a chance to try this on the other (unbranded) motherboard
that gave me trouble.