I've managed to solve this as I realised that the 'padding=true' attribute (used on ion-content directives) simply adds the '.padding' class, which is provided as part of Ionic's default CSS.
In which case I simply surround any buttons that I wish to be 'button-block' but with side padding (like in the Ionic docs) with a div and add the padding class to this div.
For example:
<div class="padding">
<button class="button button-block button-calm" ng-if="user.userType == 'carer' && connectedPatient != null" ng-click="disconnectFromPatient()">
Disconnect from Patient
</button>
<button class="button button-block button-calm" ng-if="user.userType == 'patient'" ng-click="goToCarerConnect()">
Invite Carers
</button>
<button class="button button-block button-assertive" ng-click="signOut()">
Sign Out
</button>
</div>Resulting in the following button appearances:
