How to get a reduction in alimony payment?

Changed circumstances such as a change in income would be grounds for requesting a modification of spousal support.  You could file an Order to Show Cause requesting a modification of spousal support.  An Order to Show Cause is a court form requesting a hearing on this matter.  You would also file an Application For Order and Supporting Declaration.  These are also court forms.  Your supporting declaration signed under penalty of perjury would state the reasons that you are seeking a modification of spousal support.  Your argument would be changed circumstances due to your reduced income which you would state in your declaration and would argue at the hearing.  After completing these forms and filing them with the court with an attached proof of service, you will need to serve the documents with the proof of service on your ex-spouse. When you file the Order to Show Cause with the court, the court will set a date for a hearing.

Since your residence is outside the U.S., you should have someone obtain these forms from the court and send them to you.  You can complete the forms and have someone file them with the court for you.  Check with the court and the judge's law clerk to find out if you can participate in the hearing by telephone so that you won't have to return to the U.S. for the hearing.

It would also be advisable to check with the court clerk in case Florida has different names for the court forms I have mentioned.

Although you don't have a W-2 or public records to prove your salary, you could still provide copies of the checks you receive to prove your salary and/or a statement signed under penalty of perjury from your employer stating your present salary.  If it is not possible to provide copies of your paycheck or to obtain a statement under penalty of perjury from your employer documenting your present salary, you would still have your own declaration under penalty of perjury stating your present salary which you could file with the court.