I'd say there are some very basic similarities. A lot of the footwork in boxing just boils down to 'move the lead leg first'. I do a lot of what I call 'opening the door' when I box which I guess you could say is similar to Nagashi. Except I take a quick step in as I do it and throw a left hook.
I guess these are just some random thoughts on correlating boxing footwork and Aikido tai sabaki, so bear with me.
I agree with you, always step with the lead foot first. But isn't stepping with the lead foot first basically the same as forward tsugi ashi?
Nagashi reminds me of rolling with a punch or a shoulder roll that sets up a counter.
Hiraki is sort of like side-stepping to cut off the ring or set up a better angle. So say you're right handed and you're sparring a hypothetical southpaw opponent, you want your lead foot to be outside his lead foot to land a straight right. A short side-step puts you in that position, so can Soto Irimi if you're on the outside.
A short Irimi is like a step jab while a long Irimi is moving inside to clinch or work the body.
Irimi senkai is a way to turn your opponent for better position if you are cornered, for example.
I have no experience in any other aikido style, but maybe Yoseikan tai sabaki isn't the same as standard aikido tai sabaki? Or perhaps I'm just reaching for common ground?