I think you are asking two questions
- Is it better to pray at a less than ideal time or after the limit?
- Is it better to pray with less kavana but at the ideal time or with more kavana at a "less than ideal" time?
The answer to the first question is that, clearly, it is better to pray before the limit (most often understood as the shekia).
The Gmara in Brakoht 29b says explicitly that one shouldn't delay minha up to the last minute for fear of missing the time (see Rashi there).
Rav David Brofsky cites the Mishna Berura as preferring that one prays individually without a minyan rather than praying with a minyan after shekia. Rav Ovadya Yosef (Yechavveh Da'at 5:22) and others (see Piskei Teshuvot 233:6) disagree but that doesn't apply to your case. See there for many relevant sources to the time of minha.
The answer to your second question is less clear to me. Kavana is very important in prayer, and one finds sources saying it is better to pray alone with more kavana than in a minyan with less kavana (Yabia Omer OC 4:9). So delaying beyond the additional time, provided you don't run the risk of missing the time limit, might be better if it allows you to pray with more kavana.
But as usual with individual halakhic questions, best is to ask a rav that knows you and the halakha well.