Company can’t insure me…do I still go for it? Any liabilities?

Remember these 3 letters: C, Y, and A.

That stands for "Cover Your A-double crooked letter. You have to be covered on any insurance no matter who you work for. That contractor is declining you nicely. You may want to stay local, but you gotta get experience. @Chinatown can probably find you something but be prepared to hit the road if necessary.