I realize that you asked this a while ago, but I found a solution (which has worked for me so far) and want to share it with you and anyone else who finds this thread.
The Reminders app doesn't have any visible settings for timezones, but it does understand them. If you export the items on a Mac, edit them to have "floating" times, and import them back into Reminders, they'll update to reflect the changes. Here's a step-by-step walkthrough:
Drag the todo (or todos: you can select more than one) out of Reminders and into the Finder.
Important: make a copy of this file. If anything goes wrong, you can drag the copy to Reminders in the Dock to get your original reminders back.
Open the
.ics
file in TextEdit (or another plain text editor).
You'll need to change three lines in the file. If you exported multiple todos, change them for each todo (they'll be one after the other). First, find a line that begins with
DTSTART
and looks like the time of your reminder. There may be other DTSTART
lines near the beginning of the file — they're part of a description of your timezone, and they'll generally be dates in the past — which you can ignore. The correct line should look something like this:DTSTART;TZID=Europe/Rome:20160519T100000
Erase everything from the semicolon up to (not including) the colon to make the line looks like this:
DTSTART:20160519T100000
Repeat the same change for the line beginning with
DUE
. Change this:DUE;TZID=Europe/Rome:20160519T100000
To this:
DUE:20160519T100000
Finally, find the line beginning with
TRIGGER
:TRIGGER;VALUE=DATE-TIME:20160519T080000Z
This represents the time that you'll actually receive a notification about the item (just like a calendar event, the notification is allowed to be before or after the actual "due" time). This line looks different from the others because alarm trigger times are required (by the iCalendar standard, which Calendar and Reminders both use to represent events) to be in the UTC (also known as "zulu") time zone, which is just represented by the
Z
at the end of the line.
Don't worry about the above paragraph, and replace the absolute
TRIGGER
time with a reference to the reminder's start time. Change the line to this:TRIGGER:PT0M
If you're in an adventurous mood, you can play with this value to set when you'll be reminded. For example, a value of
PT-1H
will remind you one hour before the time on the reminder, and PT10S
will remind you ten seconds after.
Make the three changes (per reminder), and save the file.
Delete all of the items you just modified from the Reminders app. This is critical: on my machine, if I don't delete them before I re-add them from the file, Reminders keeps the old timezone.
Open the modified .ics file with Reminders (either by dragging the file onto its Dock icon, or by right clicking and using Open With…).
Finally (whew!), when Reminders asks, select the list you want the modified todo(s) to live in (normally the same list you exported them from), and click OK.
If you use iCloud, the updated reminders should sync to your other devices within a few seconds. If everything went well, your modified reminders should look the same! An easy way to test is to change your computer's timezone: if the reminder's time stays the same, it worked! You can make a fresh, untweaked reminder in the same list and compare how they behave when you switch timezones.
I wrote this answer while traveling and a little tired, so feel free to ask for any clarification or report problems. Hope it's helpful.