That's pretty similar to the results that I was receiving with my Linksys. I hated the reboot mess, and figured that my wife would never be able to get it working on her own if required.
Had the power button set up the same as you. Had to disable powering down USB NIC on suspend, otherwise tended to run into the problem with the card not coming up properly as with initial reboot.
Are you having any problems streaming mp3's? I did, most of mine were gogo compressed 128Kbps/VBR. I could not get it to play a looped Samba mounted playlist overnight. Most times it crashed within a few songs.
Are you able to download large files via web or ftp? I made four attempts at downloading my printer drivers off Epson's site. This was a ftp connection with throughput that was quite high. It would crash in different places each time, but would always crash.
Lastly, I mounted a rather large mame roms directory on my Samba server. I've got over 2300 rom images in one directory. I tried to do a game audit with the Linksys, it would never complete. My other mapped drives (mp3's, screensaver images) would just stop responding after the attempt. The audit would finish, but it would say that all the zips were missing roms, I think that it could not open any of the zips and this is how mame interpreted what it was experiencing.
The Linksys seemed to be fine for general web browsing and copying files via SMB, however, you could count on it failing when the combination of high network load and high processor load were both present.
The driver that I was using came off Linksys' web site usb100tx.zip. The .inf file has a date of May 17th, 2000, and incidentally says that it is for Windows98. I did not do an checksum on them, but it looks like the files in the WindowsME and Windows98 directories in the .zip are the same. I believe that this adapter could work reliably under WindowsME, though the drivers aren't up to snuff without a little more horsepower than the Webplayer can provide.