Let's say I'm cruising on a magnetic course of 150, so I'm flying at 7,500 feet. Then I need to fly for 6 miles on a magnetic course of 210, then back to 150. Do I need to switch to 8,500 or 6,500 for the short 6 mile leg, or is it better to stay at 7,500? And if I need to switch altitudes for the short leg and I'm getting flight following, do I need to request an altitude change for the short leg and then request to change it back when I resume a course of 150?
In the case presented in the question, I would not change altitude. Why not? I would most probably be cruising at or above 120 kts. So a 6 nm (I assume miles was referring to nm in the Q) leg would take a whopping three minutes or less. To preoccupy myself with cruise descent, a minute or two of level flight and then cruise climb back to previous alt...
I would much rather broadcast my position, my intention to fly a short leg at hdg x, altitude y and then continue with hdg z. Instead of being busy with alt changes (depending on acft a handful of check items), I would be maintaining extra vigilant lookout for this rude three minute violation of rules.
Then I would just wait for the call from the local aviation administration authority. Bet my bottom dollar I would not get one.
P.S. on a check flight I would change altitude. For obvious reasons.
As you are using the term flight following I'll assume you are in the US. Flight following is an advisory service, you tell them your intentions and they give you any traffic information you may have. If you are changing altitude or course you tell them, you do not ask permission because they cannot give it.
FAR 91.159 clearly states what altitudes you should be at using the semi-circular rule:
Except while holding in a holding pattern of 2 minutes or less, or while turning, each person operating an air-craft under VFR in level cruising flight more than 3,000 feet above the surface shall maintain the appropriate altitude or flight level prescribed below, unless otherwise authorized by ATC
So if you will be flying 3000ft or more above ground level you will be expected to fly the semi-circular rule, there are no exceptions made except those listed above. From a practical perspective you'll spend more time climbing and descending than at the other altitude so I think it's a fair question, the answer is to make the altitude change.