If I'd have had to do a rewrite with the same general idea...
1. Keep the Alien count at one
2. Use a smaller community
3. Focus on a father/daughter unit, with this unit encountering the Predator
4. Use Kelly's awkward return to civilian life to develop the settings and civilians
5. Explore the PredAlien's reproductive method, but in a different way
6. Use places with subtext for the creature battles
7. Use the town's call for help as the method by which The Company finds out about the Alien
8. Forsake the "boss fight" for human input in the PredAlien's demise
9. Allow the Predator to escape
10. Have the Company use its influence to cover up the massacre
My rationale probably needs to be explained in this, eh? Well, for starters: I think one Alien is enough. It's scary when one creature turns everything on its head. Exploring the Alien less as a viral plague and more as an urban myth given life would be really interesting, and it would allow the fights to have an unknown feel to it. I would have liked to see its rampage occur in a very small community, one where escape is much more difficult due to seclusion and where help isn't about to come anytime soon.
I would have liked to see some threads to the original Predator, which is why I proposed the family archetype. The way I see it is that the first film was a giant lesson in masculinity. One of the things it skims over is how the man's man protects the weak and is more Superman than Ubermensch. That was a parallel to the honor-gone-wrong Predator, which showed some cowardly traits. Ridley only skimmed over the maternal feels in his film with Ripley and her cat, but Cameron picked up on a theme and ran with it. I don't see why a Predator film can't have the same depth, working upon the Dutch/Anna dynamic present towards the end. Making the weaker one a relation to the male adds emotional impact and gives the male and the Predator both contrasts and a reason to have epic confrontations (given that you can set up the peril in such a way that the Predator isn't stalking humans for no reason when it could be fighting the PredAlien).
The soldier-coming-home idea is not bad if you look at it a certain way. If you were to have this small community as anti-war, I imagine a vet wouldn't be treated well. You can create the feel of a town that is perfectly content with ignoring the world around them to make their later plea for help one of desperation, and add depth to both sides in the process. Make some enmity, and soon you have characters that both shape the plot and make you want to see some folks get sliced 'n diced in a satisfying way.
The reproductive system...I have no issue with it being new, but I want one that plays off of body horror. It's just an idea and not one that everyone would like, but perhaps the PredAlien from the crash could be severely compromised. Thus, to continue on the cycle it would have to implant its seed into a single host before it just breaks down. This way, you could both give a small wink to Alien and open up hybrid possibilities. Will it implant a human? A dog? What? Who knows? It would give you the feel that you'd never quite know if the Alien was dead for good or still had a trump card someplace, and the single seed aspect puts the idea on a leash so it doesn't become like a plot device.
When I say that the settings could have subtext, I mean that you can have duels in churches and hospitals. Set up places that you can see the irony in, or that make you feel like the Alien and Predator are contaminants, truly extraterrestrial. While the film used the hospital, I would've played off of the wounded civilians being accosted yet again by the space monsters. Keeping the feeling that the audience can't expect any one place of safety to be safe for long is better than editing everything at a cheetah's pace.
The rest speaks for itself, and I've gotta go eat so I'm rushing. But that'd be a little of my ideas.