0.001 ppb/year sounds unrealistic to me - by a long way. Looking at the specifications of a high-end frequency counter from Keysight, with an optional ultra high stability oven, its 50 ppb/year
Keysight specs are pretty conservative, so we might assume they actually achieve 5 ppb/year, but what you would like to get is 5 000 times better than that.
The datasheet for the Stanford Research PRS10 rubidium oscillator gives (5 x 10^-11 / year), which is 50 times worst than you would like to get.
I know you laughed at my earlier suggestion of using an LTZ1000A, but even with that, you are not going to achieve anywhere near what you want.