@Steven was kind enough to help and was able to put together this script that almost works but tapping the button doesn’t do anything:
<script type='text/x-handlebars' data-template-name='composer'> {{#composer-body composer=model showPreview=showPreview openIfDraft=(action "openIfDraft") typed=(action "typed") cancelled=(action "cancelled") save=(action "save")}} <div class="grippie"></div> {{#if visible}} {{composer-messages composer=model messageCount=messageCount addLinkLookup=(action "addLinkLookup")}} {{#if model.viewOpenOrFullscreen}} <div class="reply-area {{if canEditTags 'with-tags'}}"> <div class='composer-fields'> {{plugin-outlet name="composer-open" args=(hash model=model)}} <div class='reply-to'> {{#unless model.viewFullscreen}} <div class="reply-details"> {{composer-action-title model=model openComposer=(action "openComposer") closeComposer=(action "closeComposer") canWhisper=canWhisper tabindex=8}} {{plugin-outlet name="composer-action-after" noTags=true args=(hash model=model)}} {{#unless site.mobileView}} {{#if isWhispering}} <span class='whisper'>{{d-icon "far-eye-slash"}}</span> {{/if}} {{#if model.unlistTopic}} <span class='whisper'>({{i18n 'composer.unlist'}})</span> {{/if}} {{#if model.noBump}} <span class="no-bump">{{d-icon "anchor"}}</span> {{/if}} {{/unless}} {{#if canEdit}} {{#link-to-input onClick=(action "displayEditReason") showInput=showEditReason icon="info-circle" class="display-edit-reason"}} {{text-field value=editReason tabindex="7" id="edit-reason" maxlength="255" placeholderKey="composer.edit_reason_placeholder"}} {{/link-to-input}} {{/if}} </div> {{/unless}} {{composer-toggles composeState=model.composeState toggleComposer=(action "toggle") toggleToolbar=(action "toggleToolbar") toggleFullscreen=(action "fullscreenComposer")}} </div> {{#unless model.viewFullscreen}} {{#if model.canEditTitle}} {{#if model.creatingPrivateMessage}} <div class='user-selector'> {{composer-user-selector topicId=topicModel.id usernames=model.targetRecipients hasGroups=model.hasTargetGroups focusTarget=focusTarget class="users-input"}} {{#if showWarning}} <label class='add-warning'> {{input type="checkbox" checked=model.isWarning tabindex="3"}} {{i18n "composer.add_warning"}} </label> {{/if}} </div> {{/if}} <div class="title-and-category {{if showPreview 'with-preview'}}"> {{composer-title composer=model lastValidatedAt=lastValidatedAt focusTarget=focusTarget}} {{#if model.showCategoryChooser}} <div class="category-input"> {{category-chooser value=model.categoryId tabindex="3" onChange=(action (mut model.categoryId)) isDisabled=disableCategoryChooser options=(hash scopedCategoryId=scopedCategoryId ) }} {{popup-input-tip validation=categoryValidation}} </div> {{/if}} {{#if canEditTags}} {{mini-tag-chooser value=model.tags tabindex=4 isDisabled=disableTagsChooser onChange=(action (mut model.tags)) options=(hash categoryId=model.categoryId minimum=model.minimumRequiredTags ) }} {{popup-input-tip validation=tagValidation}} {{/if}} </div> {{/if}} {{plugin-outlet name="composer-fields" args=(hash model=model)}} {{/unless}} </div> {{composer-editor topic=topic composer=model lastValidatedAt=lastValidatedAt canWhisper=canWhisper storeToolbarState=(action "storeToolbarState") onPopupMenuAction=(action "onPopupMenuAction") showUploadModal=(route-action "showUploadSelector") popupMenuOptions=popupMenuOptions draftStatus=model.draftStatus isUploading=isUploading allowUpload=allowUpload uploadIcon=uploadIcon isCancellable=isCancellable uploadProgress=uploadProgress groupsMentioned=(action "groupsMentioned") cannotSeeMention=(action "cannotSeeMention") importQuote=(action "importQuote") togglePreview=(action "togglePreview") showToolbar=showToolbar afterRefresh=(action "afterRefresh") focusTarget=focusTarget}} <div class='submit-panel'> {{plugin-outlet name="composer-fields-below" args=(hash model=model)}} <div class='save-or-cancel'> {{#unless model.viewFullscreen}} {{composer-save-button action=(action "save") icon=saveIcon label=saveLabel disableSubmit=disableSubmit}} {{#if site.mobileView}} <a href {{action "cancel"}} class='cancel' tabindex="6" title="{{i18n 'cancel'}}"> {{#if canEdit}} {{d-icon "times"}} {{else}} {{d-icon "far-trash-alt"}} {{/if}} </a> {{else}} <a href {{action "cancel"}} class='cancel' tabindex="6" >{{i18n 'cancel'}}</a> {{/if}} {{/unless}} {{#if site.mobileView}} {{#if whisperOrUnlistTopic}} <span class='whisper'> {{d-icon "far-eye-slash"}} </span> {{/if}} {{#if model.noBump}} <span class="no-bump">{{d-icon "anchor"}}</span> {{/if}} {{/if}} {{#if isUploading}} <div id="file-uploading"> {{loading-spinner size="small"}}<span>{{i18n 'upload_selector.uploading'}} {{uploadProgress}}%</span> {{#if isCancellable}} <a href id="cancel-file-upload" {{action "cancelUpload"}}>{{d-icon "times"}}</a> {{/if}} </div> {{/if}} <div id='draft-status' class="{{if isUploading 'hidden'}}"> {{#if model.draftSaving}}<div class="spinner small"></div>{{/if}} {{#if model.draftSaved}}{{d-icon 'check' class='save-animation'}}{{/if}} {{#if model.draftStatus}} <span title="{{model.draftStatus}}"> {{#if model.draftConflictUser}} {{avatar model.draftConflictUser imageSize="small"}} {{d-icon 'user-edit'}} {{else}} {{d-icon 'sync-alt'}} {{/if}} {{#unless site.mobileView}} {{model.draftStatus}} {{/unless}} </span> {{/if}} </div> </div> {{#if site.mobileView}} {{#if allowUpload}} <a class="btn btn-default no-text mobile-file-upload {{if isUploading 'hidden'}}"> {{d-icon uploadIcon}} </a> {{/if}} <a href class="btn btn-default no-text mobile-preview" {{action "showPollBuilder"}}> {{d-icon "chart-bar"}} </a> <a href class="btn btn-default no-text mobile-preview" title="{{i18n 'composer.show_preview'}}" {{action "togglePreview"}}> {{d-icon "desktop"}} </a> {{#if showPreview}} {{d-button action=(action "togglePreview") class="hide-preview" label="composer.hide_preview"}} {{/if}} {{else}} <a href {{action "togglePreview"}} class='toggle-preview'>{{{toggleText}}}</a> {{/if}} </div> </div> {{else}} <div class='saving-text'> {{#if model.createdPost}} {{i18n 'composer.saved'}} <a class='permalink' href="{{unbound createdPost.url}}" {{action "viewNewReply"}}>{{i18n 'composer.view_new_post'}}</a> {{else}} {{i18n 'composer.saving'}} {{loading-spinner size="small"}} {{/if}} </div> <div class='draft-text'> {{#if model.topic}} {{d-icon "share"}} {{{draftTitle}}} {{else}} {{i18n "composer.saved_draft"}} {{/if}} </div> {{composer-toggles composeState=model.composeState toggleFullscreen=(action "openIfDraft") toggleComposer=(action "toggle") toggleToolbar=(action "toggleToolbar")}} {{/if}} {{/if}} {{/composer-body}} </script> His potential reasoning was: “It only works if we use the poll button of the composer before. I think it’s because Discourse will only trigger the action showPollBuilder (this is what opens the poll builder) after we trigger the action onPopupMenuAction (the icon that open the list of actions in the toolbar, like hide details, blur spoiler, build poll).”
Would anybody mind taking over? 
(Thanks again Steven for the super generous assistance!)


maybe there is a better way to find the first selector without hardcoding the options title, in case this would be an issue.
Also an option.