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Regarding Involuntary Promotion trigger timings, when I shift the upgrade and damage counters to the returned character. Do I get to choose to shift the damage counters first followed by the upgrades since they are both my triggers?

No part of Involuntary Promotion is a triggered ability. The instructions are all followed in order and the damage counters and upgrades are moved at the same time.
Source: Wizards of the Coast (2019-11-09)    【Link to Ruling】
Tags: Involuntary Promotion