Can you not prepay the card to make more room?
Nope, card only lets me pay what I owe.
I spend a lot on credit cards for business and mfg. spending.
No issuers I know of will not accept prepayment/overpayment via their site.
Amex is easiest. Right on their site, you can "Check you spending power" (Account Services>Credit Management). In my experience, they will auto approve 50% over your credit limit though lately I've been noticing it'll go to 100% over for me.
Amex also allows pre-payment but you need to initiate it externally (e.g. your bank's bill pay) to create a credit balance. That will increase your limits. All banks will accept the check but not all will allow a larger charge. BoA definitely does not accept the larger charge. I can't recall specifically for USBank, Citi, Chase, and Barclays.
As you can see here, Amex really does make it easier to spend vast sums of money than the others.
If you have multiple cards with an issuer, most will let you move credit line between them. BoA is spotty here. Chase is easy. I think Barclays is easy too.
The fall back here is multiple charges over time and/or over several cards which, depends of course, on the payee accepting that. I'd wonder a little about any warranty impacts if executed this way. In a home renovation, I'm doubt there's any coverage anyway for that.
If you do call and request a higher credit line, this usually results in a hard credit inquiry just as though you'd applied for a loan. Worry about this is very overstated unless you're less than 90 days from seeking credit elsewhere (e.g. mortgage, HELOC, auto loan, another credit card). If you are less than 90 days away, impact it's very contextual to the type of loan, issuer, and your own credit.