I'm being conservative here, too.

I'll have to go with the assumption that
Arcturus is heading off in a vector
that's nearly perpendicular to [which means it has an interesting, highly-eccentric galactic orbit] the motion of our Solar System around our galaxy.

Problem is...I can't find any good star emphemeris-tables or catalogs in the public libraries anymore to indicate the direction and trignometric
values of the motion of Arcturus across the celestial sphere.
It's a shame.
Still...I managed to get a bit more data on Arcturus
[its' radial-velocity is close to +90km/sec].
Tangent^-1[90/121.2] = 36.6 degrees.

Then Arcturus has a declination a little over +19 degrees...And then there's the nearly 23 degree difference between the celestial-equator & the
"plane of the ecliptic".
Starting to get tangled and confusing?
Yes it is...but I'm not giving up so easily....YIKES!!!

Jacob