I would think you could get to 2700 fps in your rifle with its 26" barrel.
The 338 AM is really not even remotely in the same class as the 338 RUM or 338 Edge. These two have roughly 110 to 117 gr of total case capacity filled to the case mouth with AA8700.
In comparision the 338 AM holds 178 gr of the same powder filled to the case mouth. Top usable powder charges for the 338 RUM and Edge will again be 95 to 100 gr range. The 338 AM will be in the 150 gr powder charge range I am predicting with top loads. This is an estimate but should be close.
This pic shows the 338 RUM on the left, 300 RUM in the middle(338 Edge parent case) and the 338 AM on the right. As you can see there is a distinct difference in case size, not only in length but also in diameter as well.
Just for comparision, the RUM cases have a head and shoulder diameter of 0.550" and 0.525". The 338 AM has a head and shoulder diameter of 0.635" and 0.617".
This oic of the case heads shows the difference as well. The 408 CT based wildcats require custom receivers because of their length and diameter.
Performance comparision, in 32" barrels you will get a 300 gr bullet to 2850 to 2950 possibly 3000 fps in the Edge. The 408 based 338 rounds will push the same bullet to near 3400 fps in this barrel length with top loads. Most data I have seen though is held to the 3300 fps range.
In my test rifle for the 338 AM, I am looking to break 3500 fps with a 300 gr ULD RBBT with its 40" barrel. More importantly I am hoping to break 3300 fps with the 350 gr ULD RBBT.
Just because the 408 based 338 wildcats are the largest practical 338 caliber wildcats out there currently does not mean they are best for your needs. For a big game rifle, it is VERY hard to beat the 338 Edge level of performance which is identical to the 338 Lapua.
When you increase to the size of the 408 case, you have many other things that must be considered and paid for in the rifle build. Price increases with every step of performance increase in most cases.
So the ultimte 338 for one job may be a totally different and even much smaller design that what may be the ultimate for another use. For this posts original question, The 338 Kahn is as large as I would recommend.