I am unable (or unsure) to find the right place to make the changes.

I'am here:

/usr/lib/python3/dist-packages/odoo/addons/account/views#

<?xml version="1.0" encoding="utf-8"?>
<odoo>
    <data>
        <template id="report_invoice_document">
            <t t-call="web.external_layout">
                <t t-set="o" t-value="o.with_context({'lang':o.partner_id.lang})" />
                <div class="page">
                    <div class="row">
                        <div name="invoice_address" class="col-xs-5 col-xs-offset-7">
                            <address t-field="o.partner_id"
                                t-options='{"widget": "contact", "fields": ["address", "name"], "no_marker": True}' />
                            <div t-if="o.partner_id.vat" class="mt16"><t t-esc="o.company_id.country_id.vat_label or 'TIN'"/>: <span t-field="o.partner_id.vat"/></div>
                        </div>
                    </div>
                    <h2>
                        <span t-if="o.type == 'out_invoice' and (o.state == 'open' or o.state == 'paid')">Invoice</span>
                        <span t-if="o.type == 'out_invoice' and o.state == 'draft'">Draft Invoice</span>
                        <span t-if="o.type == 'out_invoice' and o.state == 'cancel'">Cancelled Invoice</span>
                        <span t-if="o.type == 'out_refund'">Credit Note</span>
                        <span t-if="o.type == 'in_refund'">Vendor Credit Note</span>
                        <span t-if="o.type == 'in_invoice'">Vendor Bill</span>
                        <span t-field="o.number"/>
                    </h2>

you can find the template in addons/account/views/report_invoice.xml in this folder you find all the views of the reports