I built a longish oven a while back. 6 kW of elements for a chamber 9" wide, 6" high and 42" long. It was very much an el-cheapo project, built using stuff I already had, and involved some very cheap IFBs that weighed about twice as much as the JM23s I usually use and therefore had about twice the thermal mass and less insulation value. They were 9" x 4.5" x 3" and I used them for the floor and walls. With a 9" width, it would have been difficult to roof it with bricks, so I used 1" of Ceramic Fiber board backed with 2" of Calcium Silicate board. I used the same construction for the door. I know I could have used a lot less power, but I don't know how much less.
Given that sword-length generally means Carbon steel and therefore needs hardening temperatures under about 1800 degF, even for EN45. For most other Carbon steels, 1600 degF would have been enough and I suspect it would have worked fine on 3 kW. If it will need to handle stainless temperatures, the higher wattages are required.
I also built a pair of ovens, 28" x 7" x 6" internally, each with 3 kW of elements that would reach 1300 degC, 2372 degF (and rising: the thermocouple/controller combination would only read to 1300 degC). They were built to be coupled together for swords and would cope with a 56" workpiece when combined. Power for the combined ovens was 6 kW.
I'd go with Kanthal A1 wire in your shoes, just because it's the way most folk do it and it is known to work well. Rod heaters might work, but I suspect you'd need elements with a low value of watts-per-square-inch to get the heat away into a chamber that is already at 1500 degF.
Stretch on the elements is not as clear-cut as all that. Generally at least a 2:1 stretch is required. If you are pinning the coils into the grooves with bent-wire U-shaped staples, you'll want to make sure there is enough stretch that the staple cannot short out a coil. It will not affect the oven performance to any noticeable extent if it does, but it tends to erode the element where it touches and will shorten the element life considerably. I aim for at least 3:1 stretch to overcome this and use staples bent from smaller wire than the coils themselves.