Is there a way to track page splits on an InnoDB table?
I don't think there is that specific metric.  However, looking at

SHOW STATUS LIKE 'Innodb%';


Some interesting things:

Innodb_pages_written / Innodb_buffer_pool_write_requests --
    over, say, 15% is "too high"
Innodb_buffer_pool_pages_flushed / Uptime --
    I/O writes per second
Innodb_buffer_pool_wait_free / Innodb_buffer_pool_write_requests --
    "wait to get into buffer_pool" - don't want that to go over about 1%


To cut back on the physical I/O, be sure to have innodb_buffer_pool_size set to about 70% of available RAM.

If you have RAID or SSD, we should discuss further.

If you have less than 4GB of RAM, consider getting more.

Indexing UUIDs is evil, even when not the PRIMARY KEY.

Please provide SHOW CREATE TABLE; I want to see the row size and table size.

TEXT and BLOB can cause issues.  Please provide SHOW CREATE TABLE.