Steve, they are giveing you short answers for a reason, not because they're upset with you. The conversion you're looking at would be very expensive by the time you were finished with it. There are many reasons for this, I'll give you a few.
The action is much to short, even as a single shot, it would be extremely difficult to get the loaded cartridge into the chamber in the first place, with a scope, even more so. Next I'm not sure if the cartrige case would reliably extract because of its excess length.
The bolt face would have to be opened up to accept the cartridge face and the extractor would have to be recontoured as it would probably break before fitting over the rim of the cartridge and then, if it didn't, probably wouldn't fit into the receiver cut out for it.
It should be OK pressure wise. I don't think "Stevens" makes a suitable action for the ultramag.
In the end, it would just be a lot cheaper, safer, easier to buy a Remington LONG ACTION or a factory rifle already chambered for the round. Another thing, the 338 ultramag isn't that much more effective, other than in our dreams, than the 338 Win Mag which will fit into the 98 action.
In the end, it will cost as much or more to convert the 98 to any 338 cartridge as a new rifle will. If you really have to have a 98, check out the Remington 798, which is a European built 98 for them.
If you really want something different, expensive, and hard to impossible to find cartridges for, there is the 338 Lapua (almost identical performance as the ultramag) or the Laseroni offerings. bearhunter