Unable to switch from HSP to A2DP on BOSE blutoot headphones

I have a Bose NC 700 pair of headphones. The device works correctly with Android and Windows (al be it more cumbersome and confusing in Windows).

Device:
Firmware 1.5.1-9303+d287f23
GUID: 5c097385-cd87-d8dd-bab9-4c726a0ac560

I am available to test.

Problem 1: I am required to click on the "connect" toggle button for the Bluetooth audio device about 20 - 30 times to make it connect. This is also true for other speakers as for example JBL Bluetooth speakers.

Problem 2: BOSE Headset/Gnome BT Audio configuration. I am unable to switch between HSP/DSP mode to A2DP Sink. The device remains connected as a communication device and not as an audio device. I remain stuck with mono sound. Though the gnome control panel indicates that I have indeed switched to A2DP Sink. However, when I click "test" I only get the mono test and the sound is absolutely unusable. Because there is a microphone on the headphones, Gnome control panel and the underlying Bluetooth service refuse to change from HSP/DSP. Clearly this is not by design.

ProblemType: Bug
DistroRelease: Ubuntu 20.04
Package: gnome-control-center 1:3.36.4-0ubuntu1
ProcVersionSignature: Ubuntu 5.4.0-42.46-generic 5.4.44
Uname: Linux 5.4.0-42-generic x86_64
NonfreeKernelModules: nvidia_modeset nvidia
ApportVersion: 2.20.11-0ubuntu27.8
Architecture: amd64
CasperMD5CheckResult: skip
CurrentDesktop: ubuntu:GNOME
Date: Thu Sep 3 13:45:22 2020
ExecutablePath: /usr/bin/gnome-control-center
InstallationDate: Installed on 2020-08-04 (29 days ago)
InstallationMedia: Ubuntu 20.04 LTS "Focal Fossa" - Release amd64 (20200423)
SourcePackage: gnome-control-center
UpgradeStatus: No upgrade log present (probably fresh install)