I mean that's one reason (the help for the attack), since I specifically mentioned siding with one side.
That's an argument against Milan, but not for the other Forge World. Milan seemed overall more productive and much more useful for our immediate needs (shipbuilding). Add to this that both of them have attacked each other repeatedly and are likely to do so again, maybe even ask us to do it once we support one side, and I see absolutely no reason why we shouldn't pick Milan.
So again, why not Milan?
The way I see it:
If the other Forge World was so successful with their "inventing" then they would have easily overtaken Milan in the last 10,000 years. But they didn't. They stalled at best. Which means they haven't got much of an advantage. Add to this our actual needs and Milan is much more preferable (once you eliminate the bias the fandom has against traditional AdMech).
Especially once you consider that our Techmarine is the man for cutting edge stuff. Nevermind the fact whether he would want to work with a Forge World that "improves" designs. Though that argument can be turned around, so take it with a grain of salt. Fact remains though that Milan is, on paper, the better choice.
If you want arguments for Smilnay, then I'll be happy to provide them. First I wouldn't go so far as to say that Milan is more productive than Smilnay. Dont't get me wrong, Milan has the quantitative edge, but Smilnay is better from a qualitative standpoint. It's almost certainly a result of their differing ideologies.
This leads me to my next argument regarding our needs. You are correct in that Milan suits our
immediate needs the best. However, once you look to the longer term, when our fleet has escorts (which we can get with the orbital infrastructure already in the plan) and our armory is a bit fuller, that's when the qualitative and ground forces edge of Smilnay starts to shine. We'll be going through ground vehicles and armaments a hell of a lot faster than we'll be going through ships at that point, and the better quality means that more of our (quite difficult to replace, with the experience lost being even more painful) Marines will survive. Plus, we need the best life support systems we can obtain to incentivize the people of Luctus to recolonize the abandoned Refuges, and Smilnay is our best bet for those.
Then there's the power blocs they support. I have to think that whichever Forge we spurn will be incentivized to push their allies to spurn us in kind. We rely on the support of the IG a whole lot more than that of the Navy, so best to support Smilnay. I wouldn't recommend falling too far into either camp though.
As for overtaking, it's a fair bit more complicated than you describe. I don't think that either Forge World is capable of overtaking the other, no matter the effectiveness of their R&D. The difference in specializations is just too great for them to directly compete with each other. That's probably a good thing for the Sector as a whole, as the one under threat of becoming irrelevant would likely do a lot of damage to avoid that situation.
TL;DR: Milan is better in the short term, Smilnay in the long term. We can't easily change sides, so best to go with the long term view.