A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Al Stewart
Date: 2022 Jun 26, 15:25 -0700
I share your pain, but here goes...
You have correctly calculated the instant of "Sunrise" as 08:08 UTC, but at that instant the Hc is definitely not zero.... the centre of the Sun is actually 49.6' BELOW the theoretical horizon, but we are able to see the Upper Limb appear at that instant due to refraction.
For compass correction by AMPLITUDE, this is done a little after Sunrise when the centre of the Sun is actually on the theoretical (Hc = 0°), when the Lower Limb of the Sun appears to be around a Semi-Diameter above the visible horizon; that would occur at ~ 08:14:43 UTC. I like to use your Option 3 as most straightforward way to calculate OK.