Are you choosing between inductors that were specifically recommended? Because parts with 6A and 20A ratings sound more like power inductors where this circuit is producing only milliamps of current, and you should probably be looking at other more important factors. If they left you to choose your own parts based on inductance value only I would be searching for 100uH RF or HF inductors that have the highest self-resonant frequency (SRF) and highest Q. If in your searches minimum SRF and Q values aren't published then you are probably in the wrong category of inductors. I would think for that low inductance value you should be able to find molded inductors with SRF values of at least several mHz and Q values over 100.
Better yet, find an online air-core inductor (or solenoid) calculator or search here for Dewster's inductance calculator spreadsheet and wind your own single-layer coils. This way you are almost guaranteed to have high Q and high SRF. 100uH shouldn't be very many turns on a small diameter piece of PVC pipe (best) or a large wood dowel (acceptable). I would start with something like a 1" diameter coil and see if the number of turns and length of coil are reasonable for you. All you need to do is wind the wire neatly keeping the ends separated from one another. It may take a little larger box, but be forewarned that it's easy to kill any hopes of success with poorly-chosen inductors. You may want to give yourself the best chance of getting it working by using physically larger inductors and working backward from that, substituting smaller parts later if you want to fit it in the small project box.
Stacking inductors is something that is done to help attain a higher inductance without lowering the SRF. This works because one of the things that lowers SRF is capacitance between the adjacent windings and the ends of the inductor, and stacking helps keeps the windings physically separated and one end away from the other. Stacking series inductors is sometimes done at higher inductance values, but you shouldn't have to do that at 100uH.
Also "axial" inductors just refers to the lead arrangement where the leads are colinear, like a resistor. It is not related to the core material, which may be ferrite or not. Radial leads are parallel to one another coming out of one end of a cylindrical package (common in many but not all electrolytic capacitors).
Maybe someone here can be more specific and simply point you to an inductor known to work in this circuit. Otherwise, if you at least consider the above factors you will increase your chance of success.