99% of Chinese EL34s came from the Shuguang factory, with the almost all of those you'll encounter over the past dozen or so years being the second generation aka EL34B. You can distinguish them by the color of the base; EL34 are black base, and the EL34B are red base. The EL34 are poor sounding, the EL34B made a most significant improvement. In fact, I consider it one of the bargains in output tubes. I will guess your Cayin has the EL34B, but it could have the earlier variant.
You may have come to conclusions on tubes based on listening to them in other amplifiers, but not having experienced the Shuguang EL34B in that lineup? I own both the Shuguang EL34B and Tung Sol EL34, and find the Shuguang much more to my liking. The Tung Sols have a much less natural and pleasing sound, in my opinion. Based on my experience with the Shuguang versus the Tung Sol, I would instead focus on the smaller tubes, and see if changing those out bring you happiness. Also, is your amplifier fixed (variable) or cathode bias (autobias)? If it's fixed bias, having the output tubes biased too cold will definitely produce a colder, harsher, less romantic / beautiful, less extended sound with poorer imaging.
Beyond that, a bit better than the new Mullards, Tung Sol, EH, and Shuguangs to my ear and at pretty much the same bargain basement Shuguang cost are the JJ EL34 and E34L, depending on the sound one targets. More or less everyone I know who has tried the Genalex Gold Lion KT77 likes them a great deal, but as you've laid out, they're significantly more expensive. At that price point, you may also consider the Shuguang Black Treasure 6CA7-Z, which I find outstanding, though different than the Genalex. Best of all, the old school Mullard EL34, but also another step or two up the price ladder, which I don't recommend for you, as I'd first move to a different amplifier