I've been traveling for EPA for 35 years. The per diem allowance in most CONUS areas and certainly in the Caribbean are outrageously high. Typical per diem (not hotel) allowance in Puerto Rico is about $120 per day. No one can eat $120 worth of food in one day, so most employees on govt travel skimp on food and most, if not all of the per diem allowance is retained by the traveler as untaxed income that is not reported to the IRS as unearned income for tax purposes.
My suggestion is to tax the total amount of the M & IE at a nominal rate of 10%. This money could easily be tracked via each employees leave and earnings statement. For tax purposes, the per diem would not effect the travelers tax bracket, so there's no penalty for traveling more than other employees, but the 10% would be a surcharge to the employees tax liability and should be applied regardless of whether the employee is due a refund or owes additional taxes.
I would estimate that the US Government pays tens of millions of dollars in per diem travel every year. A 10% tax on this unearned income would help offset government operating expenses.