average speed for a custom section

You have couple of options:

• Use the Lap button to tag the section of your interest. You will then see the lap average in Garmin Connect
• Use the Segments feature. Define the Segment of your interest, and you will get the stats and rankings (personal and global) in GC
• Use the Trim function - you can adjust the starting and ending points of the activity, and you'll see the time and avg. pace in real-time
• Some 3rd party services linked to GC, such as Strava often offer more complex analysis of your activities 

Open the concerned activity in Garmin Connect Web.

Gear icon → Trim Activity

Do you have Strava segments enabled? If so, you'll need to enable Garmin segments to view them in Garmin Connect. Training & Planning → Segments → "Switch to Garmin Segments." After enabling, you'll see a Segments tab at the bottom of the activity page.

To elaborate on some 3rd party options:

- Strava: syncs with Connect

-- has a feature on computer (not tablet or phone) called Analysis Graph. For running this shows pace, HR, cadence, and temperature, graphed by your choice of time or distance (it's easy to switch between the two). You can highlight a section of time or distance to show average and max values for that section. I assume it would show something similar for cycling. This feature does have an issue where it includes pauses on the graph, meaning that your stats will be skewed if you select time which includes pauses.

-- You don't need a premium subscription for this feature

- runalyze.com: syncs with Connect

-- Doesn't have a mobile-friendly site, but most features will still work on phone or tablet, except those which require a mouse/trackpad

-- Allows you to highlight section of the graph (by time) to show average pace. This feature requires a mouse/trackpad (whether it's on a computer, tablet, or much more unlikely, phone). Does not include pauses on the graph

-- Also has a feature which temporarily chops up your activity into laps of custom distance/time (the laps can be different sizes, too). e.g. To see what you want in your example (8:27-17:42), you could set the 1st lap to 8:27 and the second lap to 9:15

-- Don't need a premium subscription for these features

Found the Trim Activity.  That is precisely what I wanted.  Thanks!

Thank you for the information! Much appreciated.