Leading from earlier discussion, I have drawn this:
Assuming thermal currents and voltages are equal, analysis suggests that Ic is variable from Ip/2 to Ip/200 (i.e., a range of 1:100) for base voltages of 0 to -5.29*Vt. Meanwhile, the diode supplies about -28*Vt, so R2/(R1+R2) = 28/5.29, or picking values, R1 = 4.29k, R2 = 1k is good enough.
Vt and Is cancel out, so it should be stable to a first approximation. I know there's a factor of alpha in everything, which can be mitigated with more transistors (e.g., Wilson mirror, darlington LTP), but that's a small error I won't bother with anyway. More important is, I don't know how much effect imbalance will have on temperature compensation. How sucky is a diode compensated, unbalanced LTP?
The other issue is getting 20*Ip into the tail. I don't want to stack up 20 transistors just to do that, that would be silly. AoE suggests resistors, which obviously doesn't work at low currents where r_e is way larger than R_E. The other choice is finding potentially wildly different transistors and hoping their emitters are different sized (e.g. 2N5088 vs. TIP31?), which is also rather silly, but has the distiction of potentially working.