I assume there is a reason you are abandoning I-10 after Biloxi..why?

heading north to avoid mexican border......

heading north to avoid mexican border......

I do not see a problem with the border as long as you are on the Interstate.

Just drove from SD over to Phoenix and back - and there are no problems along Freeway 8 - even though it does pass within miles of the border with Mexico. If you drive during the day and have a cell phone - no problemos.

Here's some joints to stop and rest for lunch on your way from FL to LA.
The best seafood in Mobile, AL is at Wintzell's Oyster House. Get off I 10 at Exit 26 A and go W on Canal Steet. Go .4 mile and turn right on S Washington Avenue. Turn right and go .3 mile to Dauphine Street. Take a right and Wintzell's will be on your right. The best BBQ in the area is at Brick Pit. Get off I 10 at Exit 15B and go N on Highway 90 for 3 miles to Demetropolis Road. Take a left and continue on Demetropolis Road which becomes S University Boulevard. Go about 5 miles from the left you took on Demetropolis to Old Shell Road. Take a right and go to Brick Pit for outstanding BBQ. For fine po boy's and fresh seafood get off I 10 at Exit 15A and go N on Government Boulevard to Hall's Mill Road just past the shopping center on the right. Take a right and go to the Boiling Point.
Wintzell's Oyster House @ 605 Dauphin St., Mobile, AL 251 - 432 - 4605.
http://www.wintzellsoysterhouse.com/
The Brick Pit @ 5456 Old Shell Rd., Mobile, AL 251 - 343 - 0001.
http://brickpit.com/
The Boiling Pot @ Suite G, 5300 Halls Mill Road, Mobile, AL 251 - 602 - 8405.
http://www.theboilingpotllc.com/
For fine southern comfort food get off I 10 at Exit 68 at Moss Point, MS and go N on Highway 613 to Tugus restaurant. Stay on Highway 90 going E from Ocean Springs, MS. Go to Market Street and take a right. Go to Ingall's Avenue and take a left. Go 3 or 4 blocks to Bozo's Grocery for fine po boy's. Go to Tay’s for the best BBQ on the coast.
For good BBQ and fun times get off I 10 at Exit 57 and go N on Highway 57 to The Shed for lunch or dinner. For fine country food for breakfast or lunch go E on Highway 90 to Ocean Springs, MS and turn right on Washington Avenue. Take your first left on Robinson Street and go to Bayview Gourmet. Fayard's has good BBQ. Ward's has good seafood and steaks. Phoenicia has good breakfast, lunch or dinner.
Tugus Restaurant @ 6909 Highway 613, Moss Point, MS 228 - 474 - 9910.
Bozo's Grocery @ 2012 Ingalls Ave., Pascagoula, MS 228 - 762 - 3322.
Tay’s BBQ @ 3602 Ingalls Avenue Pascagoula, MS 228 – 205 - 2167.
http://www.facebook.com/pages/Tays-BBQ/183971898302626?sk=info
The Shed BBQ and Blues Joint @ 7501 Hwy. 57, Ocean Springs, MS. 228 - 875 - 9590.
http://www.theshedbbq.com/ordereze/intro.html
Bayview Gourmet @ 1010 Robinson St., Ocean Springs, MS. 228 - 875 - 4252.
Fayard's BP @ 6905 Washington Ave, Ocean Springs, MS. 228 - 875 - 1020.
Kenny Ward's @ 1504 Government St., Ocean Springs, MS. 228 - 818 - 4505.
McElroy's on the Bayou @ 705 Bienville Blvd. 228 - 818 - 4600.
Phoenicia Gourmet Cuisine @ 123 Government St., Ocean Springs, MS. 228 - 875 - 0603.
Continue on Highway 90 to Highway 49 N in Gulfport, MS. Take a left and go one block to 13th Street and turn left to Half Shell Oyster House for fine fresh seafood for lunch or dinner. Or continue on Highway 90 to Cowan Road which is E of Highway 49 in Gulfport, MS between Gulfport, MS and Biloxi, MS. Go N on Cowan Road to W Pine Street. Turn left and go 3 blocks to Washington Street, Turn right and go to Blow Fly Inn where the local's dine on fresh seafood for lunch or dinner. Continue E on Highway 90 to Caillavet Street just E of I 110. Turn left and go N to Howard. Turn right and go one block to Old Biloxi Schooner for good po boy's. For fine fresh oysters and good seafood continue E on Howard to Fillin Station for lunch or dinner.
Half Shell Oyster House @ FL 1st, 2500 13th St., Gulfport, MS 228 - 867 - 7001.
http://halfshelloysterhouse.com/
Blow Fly Inn @ 1201 Washington Ave., Gulfport, MS 228 - 896 - 9812.
http://www.blowflyinn.com/
Ole Biloxi Schooner @ 871 Howard Ave., Biloxi, MS 228 - 435 - 8071.
Fillin Station @ 692 Howard Ave., Biloxi, MS 228 - 432 - 5565.
http://www.fillinstationbiloxi.com/
Continue on Highway 90 to Darwell's Cafe in Long Beach, MS for good lunch or dinner. Darwell's was featured on Diners, Drive In's and Dives. Continue on Highway 90 to Shaggy's Harbor Bar and Grill across from the Pass Christian Yacht Club for good fresh seafood, cold drinks and nice music. Get off I 10 at Exit 2 at Bay St. Louis, MS and go E on Scenic Highway 90 to Trapani's for fine fresh seafood for lunch or dinner.
Darwells Cafe @ 127 East 1st St., Long Beach, MS. 228 - 868 - 8946.
http://www.darwellscafe.co
Shaggy's Harbor Bar and Grill @ 120 S. Hiern Ave., Pass Harbor, Pass Christian, MS. 228 - 452 - 9939.
http://www.shaggys.biz/
Trapani's @ 116 N Beach Boulevard, Bay St. Louis, MS 228 – 467 – 8570.
http://www.urbanspoon.com/r/159/951055/restaurant/Gulfport/Trapanis-Eatery-Bay-St-Louis

Not sure what the point is in recommending dozens of restaurants when the OP has stated he wants to drive hard and just get there.

As for avoiding the Mexican border, that's a non-issue unless you are trying to avoid the occasional interstate checkpoint. There's really no safety issue on driving the shortest route which goes close to the border at times. It's up to you but I'd take the shortest route instead of adding more miles to a really long drive.

Your mileage is doable, many interstates are 70 mph or higher so you can make good time.