There is another way much shorter to get to the Split Mt. trailhead. From HWY-395 exit on Fish Springs and drive to Tinemaha Campground. The road is relatively new and easy and ends at the campground. Park and leave your car, and then check out the only 4W drive road heading west, either by hiking or biking to trailhead. It is straight forward, and you would not get lost like the other approach from Big Pine where there is a maze of 4W road.
I did it with my electric unicycle to check out the approach in 2019, and there was a gate blocking car just before the trailhead, and the 4W drive road was not good but OK for a bike.
To avoid getting your car stuck, I still advice you to ride a bike to the trailhead. It will save you energy for the hike to the Split Mt. Just lock you bike on the trailhead sign post, or find a small tree off the trail to lock your bike. I have not attempt Split Mt. yet. It is on my list.
When I did the JMT hike, the Split Mt. seems much easier to get to the top from the west side. Perhaps you can combine the two, hike a section of JMT, and climb Split Mt.