På Garmin's forum:
Edge 705 Elevation Not Correct
Yes, it is a "workaround", but I've carried out some investigations. I outlined them on another thread.
Get your 705 switched on in a clear area with good satellite reception and leave it for a while to settle down.
Go to Menu/Save Location
The screen should show a waypoint number - in my case 001 and the date, followed by the lat/long.
Below that should be your elevation. If it is incorrect, select it and set it correctly.
(I've since discovered that if you don't know your elevation, select Avg at the bottom left of the screen. The screen then changes and it assesses your position and elevation. When happy, press Save)
When your elevation is correct, select OK.
You have now saved a waypoint of your present location.
Go back to the normal screen, and press Start.
Your elevation - if it were incorrect to start with - will flip to the correct elevation you've just set.
Your elevation should remain correct.
(I found that I could delete the waypoint and the elevation would remain correct.)
You can then delete the little bit of history that you've just recorded.
Later, I deleted the waypoint as it's not needed. Perhaps you can set your home location and leave it, but I don't always start my rides from home, and where I do start them, I may not know my elevation to know whether 705 has it right in the first place. By selecting Avg, it at least has a chance of being right.