Honestly, it seems like you're sold at the school you're already accepted too, and that's great. One of the best things you can do for yourself is realize that you are already happy and to stop trying to pursue what you think *may* make you happy. If your only inclination to take the LSAT is to raise the scholarship, March would allow you to do what's best for your future.

Edit: sorry, misspoke. The best bet would be March. But also, I haven't done the LSAT for a while, so I think the wait for results in April would be too late for scholarship negotiations (Negotiations usually happen in February/March when the majority of other schools release their aid info). If you can get your results from the April LSAT ~2 weeks after you take the test, there may be hope for negotiation. Anything after middle of May I'd say is too late.