Not sure about using the powered antenna jack? I thought I read somewhere, possibly on one of the many eham.net reviews that it did not work out well?
What about using a reel antenna attached to the radio's antenna? you could possibly make your own antenna and plug into the adapter?
Reel Antenna:
RADIOS4YOU PORTABLE SHORTWAVE RETRACTIBLE REEL ANTENNA - eBay (item 260336636939 end time Nov-17-09 20:05:29 PST)
I use a Sony AN-LP1 with my DX-398 its a keeper and still available:
Sony AN-LP1 Portable Active Antenna - eBay (item 140352031297 end time Oct-22-09 18:58:22 PDT)