I have no idea about whether or not those are rewraps. A bunch of Efests are rewraps too as far as I know, so... There's that. Either way, assuming all of the number figures you have are correct, you can easily check if that information is right yourself by doing the manual calculation. The formula for figuring out a battery's maximum draw capability (in amps) is:
(battery mAh rating)/1000 * C-rating = amp limit
With the information above, that would be 700/1000 * 15, which comes to 10.5A. So yup, looks right.
Newer AW 18490s/18500s have an amp limit of 18A, so that would be a much better bet. IN THEORY you could build down to around .35ohms while still leaving yourself a decent amount of headroom.
HOWEVER (and it's a big however), I don't ever really recommend sub-ohming beyond .9 or so with 18490s as a general rule. I don't even love recommending low builds on single 18650 mechs even though I'm well aware lots of people do it. IMO, if you like your current
mod you should still get an AW 18490 with the 18A limit but maybe in terms of resistance, consider a higher build than you have now. With the right build you can still get a very satisfying vape while still upping your resistance and taxing the battery less. If you want to build lower with a mech, I would strongly suggest investing in either a 18650 tube mech with a good, high amp battery, or-- even better-- a dual-18650 for this purpose. 18490/500
mods have their place but they are really not meant for crazy low builds. Seeing as technically anything under 1ohm is subohm, a good 18490 can sub-ohm... But there are far better options for any builds that go lower than you are using now, and even that is lower than I would typically use on a 18490, personally.