How do I put a thermometer on a contribution page?
Seems like it works well for you to copy and paste the embed code onto the contribution form, there are just certain redundant bits you'd like to hide.
You could add some generalized global rules for this to your website's css. e.g.

form.CRM_Contribute_Form_Contribution_Main .crm-contribute-widget h5,
form.CRM_Contribute_Form_Contribution_Main .crm-contribute-widget .crm-comments,
form.CRM_Contribute_Form_Contribution_Main .crm-contribute-widget .crm-campaign,
form.CRM_Contribute_Form_Contribution_Main .crm-contribute-widget .crm-contribute-button-wrapper {
  display:none;
}