JMP-1 is not rated for 600 ohm loads. Maybe it will... ask Fred.
If it will: it makes twice the maximum level that the JT-11SSP-6M can take with low bass distortion.
> can I get 2 isolated 1:1 outputs?
Be very clear: are you talking ONE amp and ONE transformer? Or TWO transformers?
How isolated?
If you just want to break ground, yes you can get two floating outputs with one transformer but at half the voltage. Maybe full voltage IF the JMP can drive 150 ohms, which looks doubtful. Or full voltage with two transformers, IF the JMP will feed 300 ohms, which is dubious.
If you need to accept a short on one output while still getting "unblemished" signal at the other output: you aren't going to get there that way. I face the problem of driving up to 5 of "my" recorders, plus feeding signal to "friends" recorders. In live concert. Shorts happen!!! After someone ruined a recording with a shorted wire, I got serious. My temporary solution is an amplifier that can drive 150 ohms, and has an output impedance of 22 ohms. Its output is well-protected up to the distribution jacks, which all have a 470 ohm resistor in series. Up to three outputs can be shorted before the amp strains. With three shorts (157 ohms) the output to the remaining recorders droops 1.14dB, tolerable. "My" recorders are fed unbalanced; "strange" recorders and especially the ones outside the booth are fed through repeat transformers to break ground.
There is still one way this can (and did!!!) go wrong. If some fool (no names) connects an OUTput to the recording bus, his signal leaks-in at 22/470= -27dB back-talk.
I would rather have a small power amplifier with less than 0.5 ohm output impedance, to put leakage down below -60dB. And a wiser man suggested "assume up to 1/3rd of outputs might be shorted at once", I have 16, so it should be able to drive 5 or 6 shorts and 470/6= 75 ohms without ANY objectionable rise of distortion.
Your case is simpler. You can only have one shorted output. (If both outputs of a 2-out box are shorted, the whole gig is off.) And you can probably ensure, or notice in set-up, if something is leaking in the "output" and causing back-talk. You have two good 600:600 transformers at good price. So get an amp that WILL drive 600 ohms. If the JMP-1 won't, add a 5534, Jensen 990, or other buffer. Hang two 470 ohm resistors on this output. (470 plus transformer loss comes to about 530 ohms, close enough to 600 ohms that a "600 ohm" amp will drive it OK.) Each resistor drives its own 600:600 transformer, and then off to whatever.
Now if one output is loaded in 10K and the other in 600 ohms, you have (10,000+530)||(600+530)= 1020 ohms, an easy load for any modern "600 ohm" output. Note that the 600 ohm load is getting about 6dB drop of voltage, but that is how matched impedances work and any box with an actual 600 ohm input should be able to deal with it.
If both outputs are loaded with 600 ohms, you have (600+530)||(600+530)= 565 ohms, OK.
If one output is shorted and the other is 600, (530)||(600+530)= 273 ohms, awful low. True 600 ohm inputs are rare, but if you expect them you should use a buffer rated for a low 300 ohm load.
If the amplifier has a non-"zero" output impedance, then level to one output changes when load on the other output changes. If you set levels before the show, and don't change connections or short things while recording, you trim this out. If you plan to step on cables while recording, and can stand a 2dB level shift (pretty negligible in speech/music), then the amplifier output impedance must be less than 132 ohms. Modern "600 ohm" outputs often have series resistors of 22 to 150 and even 300 or 600 ohms, so you want to check this point. If capacitor-coupled output, the resistor plus output cap must be under 132 ohms total impedance at the lowest frequency you care about, which implies that 100uFd may not be enough to keep bass level constant to one output when shorting/unshorting the other output, even though 47uFd is normally plenty on "600 ohm" output coupling caps.
> What is a repeat coil, anyway?
An old old term from telegraph, adopted into telephone lingo. Mostly a 1:1 line transformer, often with center-tap.