Any other option than the best bodies and the fastest glass for nightlife with no flash?
Unfortunately, those are demanding conditions, and to get better results than you are getting with the gear you have, you need the next level of gear.
The body with higher ISO will help. Faster glass will help. Flash will help. All three together will give the most versatility.
Flash will help the most with what you currently have. Since flash is out, you've got to look at glass. Shooting wide open on fast glass is demanding on the focus system, which will be strained in dark conditions (true on any body, but more true on some than others - like the 6D with a 'see in the dark' centerpoint). It is also demanding on you since the DOF will be very slim and you'll have to manage that.
For the cost of the 70-200 F2.8 II, you could make the change to FF. Get a 5dMK II, new or used, and a good prime like the 40mm 2.8 panckake, or maybe the 35mm F2, or even one of the faster MF lenses from Samyang/Rokinon. If you go used (which you said is hard in your location), you might even pull off a used 5DII and a new Tamron 24-70 2.8VC lens. The sale of your current gear would bring some of that cash back.
You're kind of riding a line here. Generally, glass first is a good idea. But under your conditions you're going to need both glass and a newer body, since flash isn't going to work for you. Hard to say which to put first. Since you're in primes territory though, I would say that you dont lose AS MUCH by going non-L as you do when you're talking about zooms. The 40 pancake is stunning, particularly for its cost. You can get some faster primes now, save money over L glass cost, and put that towards the FF body you're going to nee.