Um zu and its subjects
The main problem with your translation is that in German you can't change the subject (subject as a part of speech) in an "um zu" clause.
You can say
Ich habe ihn hier hinstellen lassen, um ihn schneller zu finden.
but you can't express with "um ... zu finden" that someone else should be able to find it. The subject of the main clause is automatically also the subject of the infinitive clause whenever you use "um zu".
If you wanted to express that, you would need to use an actual Nebensatz with "damit":
Ich habe ihn hier hinstellen lassen, damit Gloria ihn findet.
In English, you have the construction "I had it put there for Gloria to find it.", but that doesn't exist in German.
Read more here (in German): https://easy-deutsch.de/satzbau/nebensatz/finalsatz-damit-um-zu/
If you insist on using "um zu", you could use a different verb that allows the subject to stay the same, but that expresses the same thing semantically, like "lassen":
Ich habe ihn hier hinstellen lassen, um Gloria ihn finden zu lassen.
(I had it put here to let (or to have) Gloria find it.)
Note that "Gloria" is an accusative object of lassen here.
Um ... zu sollen
Moreover, because the subject of an "um zu" clause is the same as the one of the main clause, the expression "um zu ... sollen" makes no sense in most contexts. "Um zu" expresses an intent, "sollen" expresses an obligation. This doesn't fit together semantically, you normally don't do something in order to be obliged to do something, or, more literally, in order to "ought to" do something. It sounds just as strange as "in order to ought to" would sound in English.
Both examples from DWDS that you found for "um zu .. sollen" are quite unusual and not idiomatic. The first one doesn't make any sense to me and looks like a bad OCR scan, the second is (kind of) correct but unusual in that it is very implicit about the two acting subjects.
Gärten oder Beete mit Trinkwasser bespritzen zu müssen, nur um erhöhte Gebühren bezahlen zu sollen, das ist wohl das stärkste, was an Gebührenschinderei geleistet werden kann.
Here, the person that has to water the plants and the person that has to pay more fees are the same, that's why "um zu" can be used, but it is unusual in that the intent that "um zu" expresses is not the intent of that person, but of a different actor, namely the unnamed municipality (?) that imposes the sewer (?) fees and makes the plant watering laws.