hi
pls dont get stressed. if there is lots of kham on it where the neckline is, plz plz don't get it altered may ruin show of the dress(and you've already said you love the dress.) So, don't fix it if it isn't broken. Plus, unless you know a tailor who does a good job on other stuff, you don't wanna just give it to any tailor...if they are not good tailor and they don't do properly - the neck of the lengha might not sit properly. I might be wrong though. How about doing this, I know it's not ideal but why not wear the necklace more choker style. To do that, tie up the necklace with the highest fastening you can get making sure comfortable as possible, then you know those see through rubber bands for hair you get in shops tie that around it so it sits like choker necklace and tuck the extra necklace inside the back of your neckline-will this creeate more space for you between top and necklace? Doesn't matter about neckline at back, your dupatta will be covering that.
If that doesn't solve problem, how about wearing as is...I know that was not the look you were going for but that is a style I've seen brides go for too.
Let us know how you get on