How much should I adapt a paper to fit another conference than where I originally submitted?
It's very hard to judge how well a paper will be received by a particular set of reviewers (which is the real question for paper acceptance).  It is certain, however, that the more that you adapt the paper to speak to the community that you are sending it to, the more likely it is to be well received.

I think that in making your decision, you would be well advised to think less about time and more about audience. Six months isn't very long to wait for a publication, so unless you've got a reason to really hurry, I wouldn't take that as a primary factor.  Instead, consider whether the work you are doing is an incremental step that would be best reserved for discussion in the focused community or whether you think it's broad and interesting enough that the larger community should hear it.  

If the former, then finish the paper now and set a reminder in your calendar for a few weeks before the deadline of the focused conference. If the latter, then go for the earlier conference and put in as much work as necessary to speak to the broader audience.  Don't just send a narrow paper to a broad conference, though: even if you get accepted, you will have less impact than if you adapt the work for the audience to which you are intending to present it.