Measuring in the single digits with a TEC LPM isn't advisable. They aren't meant for that sort of measuring. I wouldn't be surprised if your Rigel and Aerotech measured differently on an optical LPM.
I vote HeNe, but I also have a love for orange, and I started my gas exploration and studies with HeNes rather than argon. So I am biased. However, I do love my tunable.
I'd say try using some alcohol and a Q-Tip or something on the external mirrors, but it looks like you tried that, given the Q-Tip in the frame.
Sometimes HeNes aren't perfect. All of mine have a different output. Hell, my 543 is perfect and crisp, and my Raman isn't even a circle, and each line has it's own profile, and it's own unique mode shifts. I can watch the 612 and 650 be in totally different TEM modes shifting all over the place. The 633 has a larger divergence than the 629 and 635 (at least, the spot is larger), and that's all on the same unit! HeNe's are just not too comparable to diode and DPSS units, they are a whole other animal when it comes to certain things.
As far as what's causing it, could be a number of things. Probably things you can't fix. One that comes to mind is a mirror slightly off centered, could be causing an internal reflection that's just off of the spot. There's pretty much nothing you can do about that.