The suggestion to say tachanun (in a place they didn’t) without putting the head down is an elegant way out; I like it, and I do it myself.
Tachanun after dark (or shkiah as per the misnagdim and minhag yerushalayim according to R’ Elyashiv) , according to kabbalistic sources , increases the aspect of “din”, and since nightime is already associated with “din”, the combination is regarded as too much; hence, no tachanun after dark.
A few more points. There are poskim who advise saying tachanun even without a Sefer Torah present, albeit without leaning.
According to many, the Yud Gimel Midos may be said without a minyan, providing they are read as if reading (leining) from the Torah.