An update, in case any other beginners find this thread in the future:

Seems the answer was that the current draw of the LEDs was overwhelming the buffers I was using.

I was reading about the CD4000 series of ICs last week, and the descriptions of CD4049 and CD4050 caught my eye:

Hex inverter gate and hex buffer gate "with strong output drivers". The datasheets even show driving an LED from a logic signal as a typical application.

So I ordered myself a bunch and they indeed solve my problem nicely. Thanks again to everyone who took time to offer suggestions!

 

An update, in case any other beginners find this thread in the future:

Seems the answer was that the current draw of the LEDs was overwhelming the buffers I was using.

I was reading about the CD4000 series of ICs last week, and the descriptions of CD4049 and CD4050 caught my eye:

Hex inverter gate and hex buffer gate "with strong output drivers". The datasheets even show driving an LED from a logic signal as a typical application.

So I ordered myself a bunch and they indeed solve my problem nicely. Thanks again to everyone who took time to offer suggestions!

The CD4049 will indeed sink an impressive amount of current, especially if you run it on 12 or 15 volts. And even on 5 volts it will light one LED quite brightly.