Ahhh,... High Speed Machining..... Fun stuff...
Ok,...
G61.1,K70: The only thing I would add to your post is the G61.1. You don't need the K70. What K70 controls is the rate of deceleration in the corners. Think of it as a percentage system (and this is a basic description for you). When you go into a tight corner or radius (all controled by parameters), the machine will hit and decelerate in that corner at 70% of the programmed feedrate. So, if you're doing 500ipm, it will decelerate to 350ipm in the corners. If you have a "G61.1,K50", then it will run at 250ipm in the corners and so on. K70 is the machine default and that's why you don't need to set it in the program. But, this is modal (when G61.1 is in use) so if you change (like when you're doing high speed finishing), you'll need to set it back to K70 to return to the default state. Any changes to the "K" value will also return to default at reset, G64 or M30. But if you're flip/flopping between G64 and G61.1 in the same program, the "K" will still remain at what you changed it to until reset, M30 or re-entering the "K70" value.
Now, for the parameters that control HSM,.... Don't change any in the beginning. You don't know what the baselines are or how the machine will react. And each machine is different (even with the same models). 99% of the time, the factory settings for servo gains, vector settings, servo tuning, and etc. are more than sufficient for most. If you're really having problems, that when you might need some tuning. For the most part though, you have plenty of control with the K setting.
I use G61.1 for every tool and therefore it's written into my post. If I need to change it (usually only for finish passes and even that is only "sometimes"), I do it at the time of machine set up.
Of course, all of this doesn't mean much unless your machine has the "2D shape comp" option. Make sure you have it.