Is it just me or is this a question being asked incorrectly in the first place?
Pesach, Shavuot and Sukkot can be celebrated abroad in different ways. For centuries Jews in exile have understood this, including Paul no doubt. God knew this when He allowed us to be in exile.
I think sometimes people with Bibles end up with very simplistic and idealistic ideas about how life was and is lived according to the Bible.
The question the OP'er should be asking his friend is whether or not an inability to perfectly attend to a Pilgrimage Festival is in fact "breaking" Torah. Secondly, does God hate people who are reasonably unable to fulfill mitzvahs? The elderly? The frail? Those living afar (a huge number then and now)? Do people go to "Hell" for not fulfilling these mitzvahs perfectly? If not, what is the punishment?
Etc etc..
I don't think his question is wrong. If anything we learn from the book of Acts and the Pauline letters is that Paul was a globetrotter. We also learn that he ploded through hardships of travel so those two things cannot be used as exemptions.
And as far as what the Mishnah says that would be Pharasaic tradition not Torah so what Paul says about not breaking Torah he in reality meant he did not break the traditions, he says so himself:
Phillipians 3:4 although I myself might have confidence even in the flesh. If anyone else has a mind to put confidence in the flesh, I far more:
5
Circumcised the eighth day,
of the stock of Israel,
of the tribe of Benjamin,
an Hebrew of the Hebrews;
as touching the law, a Pharisee;
6Concerning zeal, persecuting the church;
touching the righteousness which is in the law, blameless.
Acts 22
"I am a Jew, born in Tarsus of Cilicia, but brought up in this city. (Jerusalem)
I studied under Gamaliel and was
thoroughly trained in the law of our ancestors.
I was just as zealous for God as any of you are today.
Acts 26
"The Jewish people all know the way I have lived ever since I was a child,
from the beginning of my life in my own country, and also in Jerusalem.
They have known me for a long time and can testify, if they are willing,
that
I conformed to the strictest sect of our religion, living as a Pharisee.