I did this many years ago on my very first bass. I made the mistake of installing the bridge P in the same orientation as the original (E/A side further from the bridge than D/G side).
I have come to dislike the split P pickup for this reason, and now only use soapbars or J-style single coils. But if you're intent on using another split P, then I strongly
suggest you install it in reversed configuration, with the E/A side closer to the bridge than the D/G side. This will tighten up the lower notes, and keep the higher strings from sounding too twangy.
Here's a pic snagged from Google: