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I don't know if I've a single or dual power supply so to be able to use it safely, do you have any clue which psu type uses the SPL Volume 2 preamp watching the inside pic here :
http://www.6moons.com/audioreviews/spl/open_big.jpg ?
It is dual. In the lower right corner of that photo there is a dual rail +/-15Vdc setup (7815 and 7915 voltage regulators). So no worries about single supply issues with the chip (common mode voltage, biasing, etc. ) No, you are not likely to damage your amp with the OPA604 or OPA627. The pinouts are the same and both run fine at +/-15Vdc. Just be very very sure you are getting the chips in the right way, with the "dot" in the corner the same as the existing one. Getting the new chip in 180 degrees reversed could very well damage some things, including popping the chip.
The TLE2071 is likely going to be the most "compatible" with the TL071 simply because TI has designed it that way. The TLE2071 is intended to be an upgrade to the TL071, and the first rule of thumb for the chip manufacturers with this kind of thing is "first do no/little harm" in terms of incompatibilites with the old chip, then improve a few things slightly with new technology. But the key word here is "slightly".
From the data sheet the TLE2071 seems to trade off some distortion (THD is slightly worse) to improve the slew rate and unity gain bandwidth. The TL071 slew rate of 8 to 13V/uS is already fine for most audio related things. Depends on how large of a voltage you are swinging. The TL071 unity gain bandwidth is a bit thin though at 3Mhz. The 10mHz number of the TLE2071 would allow more distortion-cancelling negative feedback. And the TLE2071 noise numbers are a hair better. Long story short, I would guess that you probably won't hear any audible differences between your existing TL071 and the TLE2071. But chips are cheap, give it a try for some DIY fun.
As for the other two chips, things are not as they seem. In my original reply to your post I had more written up suggesting the OPA604AP as a better audio chip, based on its data sheet specifications. But then I remembered this set of EE Times articles last year by Douglas Self which reviews all 3 of these JFET chips. Definitely worth the time for a read-through if you haven't already. There are 3 pages, click the page link at the bottom to get the other two pages:
http://www.eetimes.com/design/audio-design/4219253/Op-amps-in-small-signal-audio-design---Part-4--Selecting-the-right-op-amp--JFET-input-types-reviewed-
From his comments the real-world performance of the OPA604 and what is in the data sheet are a complete miss. From his comments and the data sheet the OPA627 would be good for DC servos, strain gauge sensors, instrumentation amplifiers, and other things that require some really good DC parameters. As for audio the distortion numbers are a bit less than the TL071 and TLE2071. Again I doubt you would actually hear much difference, and in this case your wallet would feel some pain with that pricey chip. But you could certainly give it a try!
So long story short, there may not be much you can do just in terms of (JFET input) op amp rolling to produce any major audible improvement. If you were doing a completely re-design, just as a thought experiment, going to a bipolar input chip like the LME49710 or even the older NE5532 would probably produce improvements on sensitive measuring equipment like an audio precision, but still may not be audible improvements. Take a look at the LME49710 data sheet and compare each line item vs. the same on the TL071 sheet. Much better in terms of audio parameters:
http://www.ti.com/general/docs/lit/getliterature.tsp?literatureNumber=snas376b&fileType=pdf
http://www.ti.com/lit/ds/symlink/tl071a.pdf