How about a whole new system whereby we get a smaller sick bank (say 100 hours a year with no verification requirement that is replenshed on one's hire date, as an example) but we are provided a much better short-term disability coverage policy (100% pay without the DPMA assist)?

You can bang-in sick for the occasional headache or the 24 hour cold with no worry and you are covered for the 100 hour event by a 100% short term disability policy which would require documentation anyway.