The conditions for receiving holy Communion are the state of grace, keeping the Eucharistic fast and to receive with devotion and attention. Just as you can receive holy Communion outside the Mass, if you can satisfy those conditions within a Mass you attend, even if late to it, you can receive holy Communion.
This would be true even in the case you describe, provided that you have no intention to evade the Sunday obligation if it were possible to fulfill, which in your unique situation it is not.
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