My experience with non-tubeless tires and rims set up tubeless (non-tubeless 1.35" Kojaks on non-tubeless Sun M14A rims, tubeless Furious Freds on non-tubeless SnoCat SL rims, tubeless WTB Rangers on non-tubeless Alex OEM rims, Monocog) is that your chances of success with non-standard tubeless setups increases in inverse proportion to the tire pressure. I have more experience with tubeless tires on tubeless rims.
With a tubeless tire on a tubeless rim, the tight and close-tolerance bead fits snugly on the tubeless rim's internal shoulders, so much so that some such tubeless tire/rims setups hold air even without sealants: ultralight 60 mm Big One on Velocity Blunt SS's.
With a non-tubeless tire you lack the tight, high-precision beads; with a non-tubeless rim you lack the internal shoulders.
You can compensate for the first and the second with lots of tape, but (again, IME) you are taking a chance that layers of tape make up for sloppy beads and absence of shoulders.
In my concrete experience: Kojaks on M14As: the only thing holding the beads to the rims was air pressure. Lose air pressure and your tires separate from the rims. 50 to 60 psi. I rode this setup for ~200 miles and then anxiety made me stop. Perhaps after several times this mileage the sealant gunk around the beads would have built up to form a airtight barrier so that a drop in pressure did not mean separate of bead and rim, but I did not wait around to find out.
F Freds on SnoCat SLs: tighter beads and lots of tape instead of internal rim shoulders. <25 psi. It worked fine from the first miles and I daresay that with sealant buildup it would have been double secure, at <25 psi.
Tubeless 3" WTB Rangers on OEM 24 mm OW non-tubeless rims, ~13 psi: with sufficient tape and sealant gunk buildup: so far, so good. I can let out all the air and the beads stay stuck to the rims -- in the garage. Out in the desert? I carry a tube; I carry this tube less for big holes that sealant won't seal than for breakaway beads when the air empties from the tubes. This has been the best of the 3 non-standard tubeless setups using 1 or both non-tubeless parts.
In summary: Low pressure, plenty of tape, lots of OS Regular at first (to dry and gunk up the bead/rimwall junction), then OS Endurance to prevent huge, heavy slabs of dried sealant inside the tire: OS Endurance tends to dry in a fine film that eventually seems to create an internal casing seal against thorn punctures even after it has dried out.