And to Ghostler's point, bad reeds are much more forgiving on lower instruments like bari, so might be tolerable there.
Actually, I have been buying brand name cane reeds for the bari, because not just any reed works.
I kid about it, but I have tried those bargain reeds (10 for $8 w/free shipping) with funny characters matching those on packaged fireworks with ratings not in common reed strength charts.
I've had better luck with my alto sax.
Recently I bought 2 boxes of 25 each Rico orange box in 1.5, because I use a wider tip D'addario Rico Royal B5 Graftonite mouthpiece.
However, I bought the proper strength Bari artificial reed, hence why it works.
But for me on tenor, Bari brand was an awful experience. It was also a painful experience since they pinched my bottom lip until it bled.
There is something wrong if you need bite pressure great enough to cut your bottom lip. I suspect the reed you were using was too hard or strong for your needs.
It should be no different in strength than for a cane reed, except you do not need to wet it.
Also given your embouchure and current mouthpiece, may be cut in a manner that certain reed geometries work better than others.
I found for example, that my Rico Graftonite C5 tenor mouthpiece did not like tenor reeds like my other tenor mouthpieces. But I slapped a baritone reed on it. Now it worked.
Apparently given my embouchure on it, its lay table was cut in a manner that the longer cut baritone reed was a better fit.
I guess some have a better suited embouchure for the Graftonite C5 than I.
Also, there is sax playing folklore that beginners use soft reeds, pros use hard.
If one uses wider tip gap jazz mouthpieces, these use softer reeds because the reed tip travels a greater distance, needs the flexibility.
One selects the reed strength given the mouthpiece and embouchure. Everyone's mouth is different.