@Steven любезно помог и смог собрать этот скрипт, который почти работает, но нажатие на кнопку ничего не делает:
<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>
Его предполагаемая логика была следующей: «Это работает только если мы сначала нажмём кнопку «Опрос» в композере. Я думаю, что это связано с тем, что Discourse сработает действие showPollBuilder (именно оно открывает конструктор опросов) только после того, как будет выполнено действие onPopupMenuAction (иконка, открывающая список действий на панели инструментов, например, скрыть детали, размыть спойлер, создать опрос)».
Не найдётся ли кого-нибудь, кто возьмётся за это? 
(Ещё раз огромное спасибо Стивену за такую щедрую помощь!)
Возможно, есть более хороший способ найти первый селектор без жесткого кодирования заголовка «Options», на случай, если это станет проблемой.
Тоже вариант.