If I were to be the guy at Microsoft wanting to handle this browser-war situation, what would be my strategy ?

If I were in Microsoft and were given the target to endorse IE v8 then following would be my approach:

1] There are various pro's/features in IE v8 which have been made especially for developers which, either have not been publicized or not put under immediate public glare. There are also many cases where people have failed to realize the importance of these features. Though Microsoft is trying their best through it's own web-site, MSDN and virtual-tech-days, it has not been completely successfully. Some of these features are accelerators, web-slices, loosely coupled browsing, recovery(fail-safe) mode, developer tools, miniature based tabs, WPF(in affiliation with silverlight), WCF etc.

The strategy to publicize the above features can be adopted due to the fact that developers pave the path for future innovation in WEB v1.0 and the incoming WEB 2.0 for users/surfers and hence they need access to some superior/extraordinary tools to achieve their intents.

Now comparing the above feature offered to developers by IE v8, Mozilla's Firefox doesn't provide any of that sort(except add-ons and customised search tags). Google's Chrome doesn't even come close to a touching distance(BETA people made it FINAL recently). Opera, Safari and Flock are in their league of their own.

2] Secondly, while trying to benchmark/compare all the browsers, people always first try to compare the speed of execution of an HTML page on every browser and subsequently then on each tabs and then conclude which of them is faster. Obviously that the most simplest method of judging.

Going by the above criteria, FF surely wins the medal. Similarly, Chrome is excellent in Javascript handling. Microsoft can actually take a cue from this, refine it and implement the same feature in IE.

Though, personally I feel speed of a web-page should not be the only benchmark on which a browser should be judged.

3] Thirdly, Microsoft's policy in embedding IE with it's imposing Live search with all of it's Operating Systems shipped till date is very much onerous on the part of it's customers. Personally speaking it's also not going down well with me and I'm sure with everyone.

Microsoft can actually plug a solution to this long-lasting problem by giving options to the users at the time of installation on which intended browser he/she wants to install.

Though the above is quite impossible but surely nothing is with Microsoft. I believe.

4] Microsoft has always been running straight like a horse fitted with flaps fitted around it's eyes to prevent any abberation. We expect Microsoft to do the same this time round as well. This browser-war is just a farce for MS and surely it will resolve this and come out victorious. We believe.

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There are several more aspects which Microsoft can look into but for now, I can only think of the above three aspects.
SIGNING OFF.
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