Yes, Harmony remotes do have the List button that will go straight to the My Shows menu.
The TiVo model I used way back when I first set my Harmony One up is TCD-648250B.
Philips Series 1 HDR212, Nov 2001, never activated (retired)
Original OLED Series 3 (Lifetime) - Nov 2006, upgraded to 1TB in 2009
Premiere Elite/XL4 (Lifetime) - Oct 2011