That specification really screams Embraer Legacy.....although the full 4,000nm is beyond this machine's scope.
Likely the best way to deal with that very occasional higher requirement is charter.....
You might also take a look at the Lineage...or A318Elite as capable of achieving those sort of higher utilisation rates, especially if you can establish an airline based maintenance regime with a local operator..but these can't be considered mid-sized.
Forget anything from the Challenger 800 series.....unless you can negotiate draconian penalties for low reliability from the seller.
A Hawker 1000 would be interesting...but getting somewhat long in the tooth and those utilization rates kill off that idea somewhat.
Do328 ....range is way not enough
Fokker 100 and any of the older 'airliners' , maybe get for low price but operating costs will kill you....
Go East Young Man.....A Russian machine......sadly not...nothing fits the bill and a Yak 40, isn't going to be welcome anywhere you likely want to travel to.
Nope....Legacy it is...