Is it permissible, Islamically, to delay one's arrival at the mosque for Fajr and Isha prayers until the middle or end of the first unit (rak'ah) of prayer, in order to avoid the fatigue caused by the imam's prolonged recitation, knowing that one is able to stand for the entire first unit if one were to attend at the opening takbir (takbirat al-ihram)? And is one sinful for intentionally doing so?

Understanding the opening takbir is recommended, not obligatory. What is obligatory is to catch the congregational prayer, not necessarily its beginning.

If the prolonged standing in prayer causes extreme fatigue that diminishes khushu' (devotion), then this is an excuse that permits praying while sitting.

As for someone who is able to stand when praying alone but is unable to do so in a congregation: - It is said: He has a choice between the two matters. - It is said: His prayer with the congregation is more preferable. - It is said: He should pray alone, standing, and this is the stronger opinion, because standing is a pillar (of prayer) without which the prayer is not valid when one is able, whereas the prayer is valid without the congregation.