I think there are three issues to unpack with respect to Reeling: the frequency that the effect gets applied, the action economy required to get rid of the condition, and the difficulty to get rid of the condition.
Frequency: Based on the math I did above, it seems like reeling may be applied relatively frequently, maybe 35-40% of the time depending on Damage Threshold and weapon used. As this is totally dependent on the damage threshold/fortitude save, this perceived problem may end up being mitigated in the future by better armor, better class saves from multi-classing into classes with better Fort Saves (particularly Prestige Classes), feats like Improved Damage Threshold, and increases in class levels. This may just be an artifact of low-level characters being a bit squishy.
Action Economy: Using your action to recover, and not being guaranteed recovery, seems rough to me. While you can still move, being sidelined for possibly multiple rounds can really hurt, especially when another shot could easily knock you stunned and I'm not sure if you could even attempt the check then (you're considered incapacitated and therefore can't take actions or reactions). So, I still think I may be an advocate of using your Bonus Action to recover. If you succeed, you can act normally (less your Bonus Action); if you fail, you can still take your actions but at disadvantage. Since you're still reeling, you are still susceptible to getting stunned.
((Also, sidebar, what are the effects of being stunned with respect to Fort and Reflex saves? In 5E, you autofail Strength and Dex Saving Throws if you're stunned. Not sure how that interacts with static defenses, knocks them down to 10?))
Recovery Challenge: Currently, barring certain feats (Shake It Off and Improved Damage Threshold), the best you can have is a +5 to your recovery check. With a 20 CON, the success rate would range from 80% (DC10) to 30% (DC20). Most characters will have, at best, a 14 CON (+2). Success rates at that point are 65% (DC10) to 15% (DC20). If that doesn't seem suitable, I would suggest changing the recovery roll to 1d20 + (Better of STR or CON Mod) + (Class Bonus to Fort Save). Since the save is capped between 10 and 20, I don't think Character Level/Proficiency or Armor bonuses should factor into it. That way, the squishy characters have a tougher time recovering, but soldiers and the like should have a somewhat easier time of it, with really meaty melee soldiers probably having the easiest time of all. At best, a single-classed Soldier would have a +7 to save with a 20 STR or CON. It might create an issue with Prestige Classes like Elite Soldier and Jedi Master, but they should be pretty hard targets and would only have +9 with a 20 STR or CON, basically auto-saving at low levels of damage, but still needing a decent roll when faced with significant damage.
Just my thoughts on the setup.
