Do we split outstanding mortgage principle if splitting the interest in half? Filing as MFS & both names are on 1098 but outstanding principle is over 500k (about 550K).

My wife and I are filing our taxes as married filing separately this year. We purchased our home in 2016 and both of our names are on the 1098. The outstanding mortgage principle is about 550K which is above the 500k threshold for married filing separately. Since we intend to split the mortgage interest by half for each of our returns, do we also split the outstanding principle so we are not penalized for it being over 500k? Or do we need to use IRS Publication 936 to calculate our allowable deductible interest since it's over 500k?