I would hold back 10% which will give you leverage and not jeopardize taking the whole amount for the tax credit. I paid for a system in March but it was substantially completed much earlier in the prior year but one small item held up the PTO. In my case I was never invoiced. The invoice is your documentation for your tax records because it and the inspection are proof that the system was completed in 2020.
While I agree this is a reasonable approach for purposes of dealing with Tesla, for purposes of the IRS, I would note that while a paid invoice and inspection are good evidence, they are not the only means of demonstrating that the system was complete. Dated images, written confirmation from Tesla the install is complete, application for inspection, and, since OP has PWs, even screenshots showing production would be good evidence the system was "placed in service" in 2020. (PWs are relevant here because Tesla usually doesn't enable app access until PTO if there are no PWs.) And, the IRS language provides "Except as provided in subparagraph (B), an expenditure with respect to an item shall be treated as made when the original installation of the item is completed." (Paragraph (B) relates to building construction/reconstruction.) So, while having an invoice is important, showing that it is paid may well not be.
I am somewhat in a similar dilemma. My solar roof install was complete and did pass inspection. Within hours I got the invoice and payment request via both text and email. I paid the full invoice.
See the link and quote above, in particular, "Except as provided in subparagraph (B), an expenditure with respect to an item shall be treated as made when the original installation of the item is completed." For purposes of the ITC, "expenditure" has a specific meaning, and it is not necessarily synonymous with payment. That also includes loans. In fact, my understand is that many solar loans, including loans from companies Tesla partners with, can include a balloon payment set to coincide with receipt of ITC credit, which is claimed in full for the tax year during which the install was completed ("placed in service".)
I would agree that what you described is the likely outcome with the IRS, and as long as the mistake, if any, was made in good faith, it probably won't be a major issue. (As opposed to somebody who tried to claim for a system that did not exist or tried to claim for clearly non-deductible expenses.) Had a similar experience many years ago where the IRS did a partial, mail audit, on a specific item. Just sent the documentation (which they already had but apparently didn't look at,) they accepted it, and that was all.
