Is an agreement with a roofing contractor binding if they don't sign also?

I don't think you understand how insurance claims work. You may find someone to do the work for less, but your insurance company is only going to pay for the invoice amount that you are charged for the repairs. If your insurance company scopes the damage at $12,000 and you have $1,000 deductible and $3,000 in recoverable depreciation, then your first check from the insurance is $8,000. If someone gives you a bis to replace your roof for $8,500 and you accept that bid and have the work performed, the insurance company will only release $500 of the remaining $3,000 recoverable depreciation. They end up keeping the $2,500 balance. It is illegal for a homeowner to profit from an insurance claim in Texas. You should not worry about who is the lowest, rather get the work done by a reputable, insured company and let the insurance company pay for your full repairs. You can probably talk your contractor into some upgrades for your home. I also would caution you about having the work done by a cheaper company and submitting an invoice for a higher amount to your insurance company. That would constitute insurance fraud in Texas.