Here in the USA, the temples nearer our home follow Tenkalai sampradayam alone. During satrumura, can we recite the taniyans as per our sampradayam? Further, can we recite the Tenkalai Acharya (because they follow Sribhasya sampradayam) taniyan?

There is no harm in reciting the solkas about any followers of Ramanuja. If it is a compulsion to follow the satrumurai order as per their sampradayam, one can certainly do so.
If they allow, it is good to recite taniyans from our tradition in that temple.