Yeah techniques like instruction re-ordering, messing with the clock, etc are legitimate options. However all they will effectively do is decrease the signal-to-noise ratio of the system; increasing the number of measurements the adversary will need to require.
The power of averaging is such that these extra security added by these types of countermeasure can rapidly drop to zero. Despite this there are some use cases and deployment environments in which this might still be worth doing.
Ultimately the game for people deploying SCA-resistant hardware is effectively to fix a period of time in which a single key is used, and add sufficient countermeasures to ensure that the attacker can't get the key within that period. 'Perfect' security isn't a strict requirement at all, nor is it possible to achieve.
The interesting work here is definitely on the measurement/acquisition side. Ultimately if it's an unprotected AES you're going to be able to exploit some leakage given enough measurements.
This is pretty consistent with recent results that attack more 'exotic' targets; the post-acquisition phase uses the same old techniques that were 'discovered' in the very early 2000's. It seems to be that once you've found the things you need to do to get clean measurements you can just use the straightforward linear-dependency related stuff or do a simple profiled attack if that suits.
This is a common countermeasure. You need to be aware that you maybe just be moving the problem. In settings in which key agreement techniques aren't used you'll be deriving new symmetric keys from an initial secret using a KDF. You now need to make sure that the KDF is DPA-resistant.
Forward secrecy is defined with respect to key agreement schemes and not symmetric crypto per se.
No algorithm is secure by design against these DPA attacks. They exploit data-dependencies.
The only 'provably secure' (e.g., on paper (+)) countermeasure you can apply to these symmetric schemes is something typically called masking. You can view masking as using secret sharing techniques to split up all intermediate computation into independent operations. To defeat masking an attacker needs to be able to re-combine the data dependent information leakage associated with all the split components. This is always a possibility.
Thus it becomes a risk/cost tradeoff. The more you mask, the more secure you become, but at a cost of speed/area/power draw.
(+) It's decidedly non-trivial to implement a masking scheme such that you get the theoretical security. This is an active research area.
The power of averaging is such that these extra security added by these types of countermeasure can rapidly drop to zero. Despite this there are some use cases and deployment environments in which this might still be worth doing.
Ultimately the game for people deploying SCA-resistant hardware is effectively to fix a period of time in which a single key is used, and add sufficient countermeasures to ensure that the attacker can't get the key within that period. 'Perfect' security isn't a strict requirement at all, nor is it possible to achieve.