Fender Strings

I recently have had problems keeping my E and A in tune during practice and unfortunately during a show. Which, conicedentally, was the first show I ever, EVER, had to tune my bass during the set.. A few days before the show I had replaced my usually Fender strings with D'Addario XL's. I loved em, but found one problem, the strings kept popping out of the nut at the end of the neck.. This was during songs!! Thank God it was only in practice. I changed to E and A fenders with the D and G being D'Addarios. This was great cause it gave me a bright high end tone and a boomin low end tone.. the only problem is that I'm having trouble keepin the E in tune. Especially when I play slap or play hard. The Fenders are .45 - .105 gauge, where as the D'Addarios were .40 - .100 (so no wonder they kept poppin out). Is there a type of string out there that gives you a bright/trebly tone from the D and G and a boomin low end (somewhat trebly) tone from the E and A? Cause I have an upcoming show and I want to get through it without having to tune.. If I wanted to tune every 3-4 songs I would have played guitar..lol Suggestions??