How to set 'path to me' or 'path to resource' as property

I’m updating an oldish, long and complicated script bundle which, will be saved and run as a stand-alone applet. The bundle contains many resource data files to be called and the script has lots of handlers. I want to replace some local variables with properties to cover all relevant handlers, some nested. I thought it will be simple but, I hit a wall: how to convert convert ‘path to me’ or ‘path to resource’ to property.
These are simple tests of what I’d like to do but any variation I tried failed:

-- test1
use AppleScript version "2.5"
use scripting additions

property myRes : missing value
set myRes to (path to me as text) & "Contents:Resources:"
property myIcon : myRes & "my.icns"

display dialog myRes & return & return & myIcon
--> myRes: "~Desktop:test property:test1.scptd:Contents:Resources:" --> OK
--> myIcon: "missing valuemy.icns" --> Wrong. The property hasn't taken the new value.
-- Obviously, this would fail:
-- display dialog myRes & return & return & myIcon with icon myIcon

or

-- test2
use AppleScript version "2.5"
use scripting additions

property myRes : (path to me as text) & "Contents:Resources:"
property myIcon : myRes & "my.icns"

display dialog myRes & return & return & myIcon
--> myRes: "HD-1:Applications:Utilities:Script Editor.app:Contents:Resources:" --> wrong
--> myIcon: "HD-1:Applications:Utilities:Script Editor.app:Contents:Resources:" --> wrong

-- The test2 fails when run in the editor as well as when saved as an app: 
-- 'path to me'  persists pointing to the editor's resources instead of its own.

What am I doing wrong? How to do it? Please help, my head is hurting.

You will get a better behavior with :

-- test2
use AppleScript version "2.5"
use scripting additions

property myRes : ""
property myIcon : ""

set myRes to (path to me as text) & "Contents:Resources:"
set myIcon to myRes & "my.icns"
display dialog myRes & linefeed & linefeed & myIcon
--> myRes: "HD-1:Applications:Utilities:Script Editor.app:Contents:Resources:" --> wrong
--> myIcon: "HD-1:Applications:Utilities:Script Editor.app:Contents:Resources:" --> wrong

-- The test2 fails when run in the editor as well as when saved as an app: 
-- 'path to me'  persists pointing to the editor's resources instead of its own.
my fakeHandler()

on fakeHandler()
	display dialog "I'm in the handler." & linefeed & linefeed & myRes & linefeed & linefeed & myIcon
end fakeHandler

In your codes, the properties were defined at compile time and in such case, as you saw, path to me pointed to the Script Editor.

Yvan KOENIG running El Capitan 10.11.1 in French (VALLAURIS, France) lundi 7 décembre 2015 16:00:27

Many thanks Yvan. That works nicely with all my real properties. I did try “” but only for ‘myRes’ not for the others. Thanks again.