Recently I needed a midline bend for a line perpendicular to the mainline, sorta like a T.

Really, do tell us about this need!
To bend a rope to the middle of another --"middle" implying
that this rope to be loaded on both (or either?!) ends (end)--,
one might try a hitch. Looking at your solution, you obviously
had sufficient slack in the line tied in its middle (to make a
clove).
In which case you might've made an eye-knot and then used
a bight hitch to that eye.
... what I came up was a midline clove hitch on the mainline and a bull hitch for the secondary line
...
What do you think?
That I'd like to understand your application. And I'm
in any case skeptical about the use of the
clove hitch--it can be temperamental and jammy.
The Bull Hitch can jam, so I'd be a little hesitant to use it in this application unless the strains are low.
But I don't think this : especially tied around rope,
there won't be any jamming --too much friction to
overcome!
The (my-named)
Janus bowline orginated from a mid-line
attachment, and that seems a reasonable solution for
consideration (again, not knowing the details of use);
just form the nipping loop in the "mid-line" and reeve
the tying-to rope through this loop, collaring one then
the other side/ends of the loop.

--dl*
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