The FAR on this is FAR 91.159:
Unfortunately the regulation isn't much of a help with your specific question. The best course of action would be to file the altitude that you initially intend on flying, and then request an altitude change when your magnetic course warrants it. It sounds like you intend on getting flight following, which is always a good idea, so you can request to change altitudes when appropriate. If ATC does not authorize an altitude change then you're still in compliance with the regulation because ATC has "authorized" you to remain at your current altitude.
I've never heard of this regulation being grounds for a violation from the FAA (by itself). Unfortunately this regulation only becomes a topic of discussion from the FAA during investigations of near mid-airs or worse.
If your path is zig-zagging across 180/360, and you're receiving radar service from ATC, take advantage of that "unless authorized by ATC." If they know your route and altitude, and don't say anything (and I have been reminded by ATC when I pick the wrong altitude for my direction of VFR flight), nobody else will care. A violation of this regulation isn't going to be filed unless ATC files the complaint, and they'd say something to you long before they'd file a "Pilot Deviation" with the FSDO.
If you're not talking to ATC, nobody will ever notice unless you run into someone. So don't run into anyone.
Unless ATC gives you a different altitude while you are getting flight following, VFR altitude is at the pilot's discretion. You don't need to tell them when you change altitude unless they've assigned you a specific altitude or told you to advise when changing altitude. Remember that the regulation applies to flights over 3,000 AGL so if you are flying over the mountains, you may not need to alter your altitude if you are < 3,000 AGL.