I think this idea has some promise, giving a good money-sink into the game which is badly needed.
1. First, I would require it to use the navigation logger that currently exists; get more use out of that game mechanic.
2. It should only be able to travel at like 1000m/s (~8x faster than current ships).
3. It should not phase through rocks or objects, if at all possible (collision should be "allowed"). This satisfies your #2 for the most part, as people will not want to activate it if they are going through a belt - but they would also have that freedom should they know a perfectly clear-path to their destination.
4. With your #5 and #6, it should cost a lot, like 1 stack of exorium per 10k distance, perhaps more or less depending on total ship weight, trading money for speed (and thus, time), and making a 250km jump cost ~125k credits at current Origin prices (remote location prices would go up, then!). This also limits overall range and use; not going to the moon like this.
5. It should be a straight line from point to point, just like the current warp mechanics.
6. I agree it should not be usable from within a safe zone or close to one ~1000m out, nor have a destination inside a safe zone; arbitrary logic, which I usually dislike, but it needs some risk involved, and some way for players to intercept if they do a lot of recon work.
7. Start and end positions should leave some trace of the warp having occurred for a while, if possible. This would allow recon as in my #6; much more likely people will re-use the same points in the future.
8. A warm-up time should be required. Maybe 1 to 5 minutes max. Again, gives some counter play.
9. A cool-down time might be good, to increase risk and counter play.
An issue with "speeds beyond the normal game speeds" is it removes people from the game. There's almost no counter play to it, and eliminates a lot of risk. EVE did a good job with their warp bubbles - and truly, Starbase can do the same, using the warp core itself in a mode which disrupts warp within a large area perhaps - and the game benefited from there being a lot of ways to interact around this mechanic.
Speed is very important to have it done right, so this is not something I'd ever want thrown together, but truly thought out in all the ways it could be abused and so on. It's so powerful, it should come with significant risks to use that almost guarantee some loss of the ship if used enough times. Meaning, if someone sees a warp-exit and places some trash objects there, the next time the warping ship comes into that position it takes significant damage due to the collision at high speed.
Tricky to do collision at high speeds, but maybe some predictive logic during the warm up and cool down period could resolve potential collisions.
Overall a decent idea, mainly for the credit and resource sink it would create. Beyond that, all sorts of things open up, like player transport options and so on. If people can hop on a transport from Origin to Markka, paying their way of ~30k credits let's say, and it will take them ~10 minutes to get there vs. the 45m-1hr they might otherwise have, it gives some good choices. In addition... the transport ship will be out of the safe zone a long time... this strengthens company relationships and makes you less likely to haul an enemy company member on your ship.
One thing to consider is player inventory weight should count towards the total fuel cost, so people aren't hauling free inventories of loot around. But anyway, like I said, lots to consider to make it work well, and it's not a necessity by any means; the game doesn't need it, and would take away from so much natural travel that it might even be detrimental to the game. Careful consideration is needed. Maybe in a few years