Driving cross country with expired tags - how to avoid police?

I'm going to be driving from Washington, DC to northern Louisiana with
an LA license plate that expired a couple of years ago. Insurance and
driver's license are okay. Any suggestions about what route I should
take or how I can avoid getting pulled over? I'm a pretty safe driver,
don't speed...going to try and make sure my car is clean and not
conspicuous...

Should I just stick to major interstates and hope a cop doesn't get
close enough to notice? What about smaller, more remote highways and
local roads? (Travel time is not a concern...)

Does anyone have suggestions about specific states, cities, or roads I
should avoid? I've heard plenty about cops in the south being worse
about hassling drivers from out of state. I've heard bad things about
Lousiana police on I-10, too, and although I won't have to drive very
far into LA, I'm concerned about getting nabbed there, where the police
will certainly know what color my tag is supposed to be.

Has anyone else done this? Any suggestions would be very helpful!