What is considered the “perfect” prefix for items like the Stinger pistol is debatable. Personally, I would recommend a Vengeful Stinger (Fire Rate+) with a Vladof grip and either a Jakobs, Torgue or Maliwan sight (no zoom). Another option would be a Purging Stinger (Damage+) with the same parts as the Vengeful. FYI, I have a set of Vengeful Stalkers (similar to the Stinger) and they work very well even without a Blurred Trickster COM. Also, you might want to consider the Stalker over the Stinger. IIRC, an OP8 Vengeful Stalker (Fire Rate+ prefix) will do more damage than an OP8 Purging Stinger (Dmg+ prefix) if both have a Vladof grip (which you would want anyway for bonus reload speed and magazine size).
The only “type” of Bekah available is Non-elemental, since the Bekah is Jakobs and almost all Jakobs weapons are NE. Your best bet is a Boss Bekah (Damage+) with a Jakobs grip and a Dahl Stock. The Dahl Stock will help with recoil control and weapon stability. The sight only becomes an issue with the Bekah if you want a zoom or not. FYI, I have an OP8 Boss Bekah that I use with my OP8 Siren and it works very well.
Lastly, I would be more concerned about the stats for the Legendary Cat and somewhat less concerned about the level. As an example, the Legendary Cat I use is OP8 and has +138% SMG Dmg and -41% SMG Accuracy. I have another Legendary Cat listed in my trade thread that is +134% SMG Dmg, -37% SMG Accuracy. It is only 4% less than my OP8 version (has better accuracy loss), and it is only level 71. FYI, the max for an OP8 Legendary Cat is +138% SMG Dmg, -41% SMG Accuracy.
Unfortunately, I play BL2 on Xbox 360 so would not be able to assist you. FYI, the Bekah behaves more like a rapid fire Sniper Rifle than a traditional Assault Rifle. The Bekah is probably the best Assault Rifle for Maya, so even if I did play BL2 on Xbox One I wouldn’t be willing to part with my Boss Bekah. But you shouldn’t have too much trouble finding someone willing to trade with you on Xbox One, especially if you are offering a Grog Nozzle.