That circuit is much better.
Note that the "proper" way that this would be done in a studio would be to use an AUX send on your console or digi-interface+daw and then recover the wet-only echo on another channel and mix it into whatever track(s) to taste. That method is superior because 1) you can adjust levels to account for the fact that consumer and even pro-sumer Reel-To-Reel machines cannot handle high level signals used by pro consoles or digi-interface+daw setups, 2) you don't run the dry part of the track through another gizmo and most important 3) you can mix in just enough of wet to taste and not add the full noise of the source output.
But I could also see how you would not want to go through all of the setup for that in which case a little gizmo like you're making is nice. Although little mixers are pretty cheap.
If you want something that integrates with the patchbay, you could do something like this:
I have one these on each of my two 1U patchbays. They are completely passive and quite effective. Output impdance is ~1K or less which is fine if you're just running into something else that will buffer.
Basically the way this "mult-mix" works is the 4 inputs mix balanced signals into a 4 output "mult" above the inputs. In this version, you have two inputs that mix equally, one that attenuates -3dB (relative to a 0dB input) and another input that attenuates -9dB (relative to a 0dB input). You can also get one -6dB mix by plugging into -3dB and -9dB (because the load is the other inputs, the -3dB input is actually not attenuated at all so you get 0dB and -6dB).
So to implement tape echo with feedback like you're doing, you would use one mult-mix (which I will call MM1) to split the dry to tape and to a second mult-mix (MM2) and then mix the tape output into MM2 (at 0, -3, -6 or -9dB). So the "input" of the whole thing is MM1's input and the "output" is MM2's output. You can also get feedback by taking the MM2 output and feeding it back to MM1 (at 0, -3, -6 or -9dB). And, as a cool side-effect, if you yank the input from MM1, it removes the load so that the output of MM2 doubles back through MM1 and suddenly you get a 100% feedback loop which causes that characteristic spaceship saturation sound. To stop the loop and go back to the mix, plug the bantam jack back in.