MS-DOS 6.22 only uses CHS (cylinder/head/sector) addressing to access disks, so it doesn't really matter if the BIOS supports LBA addressing. The CHS BIOS access method is also known as INT 13h, not to be confused with extended INT 13h which uses 64-bit addressing. The CHS BIOS interfaces MS-DOS uses for disk access supports drives up to just under 8 GiB, so this also about the limit for MS-DOS. (A bug in MS-DOS means that it crashes if a drive has 256 heads, so its limit is a bit smaller than the BIOS limit but still almost 8GB.)
The limit you've encountered is due to the intersection of the BIOS and IDE limits on CHS addressing being much less than either individually. The BIOS supports addressing up to 1024 cylinders, 256 heads and 63 sectors, while IDE supports up to 65536 cylinders, 16 heads and 255 sectors. Taking the minima of these three pairs (1024 × 16 × 63) gives you the 504 MiB limit.
To get around the 504 MiB limit many BIOSes supported CHS translation, where they converted BIOS CHS addresses to IDE CHS addresses using some sort of transformation. Apparently though your BIOS doesn't support this, otherwise the drive probably would've worked. You should check to see if your BIOS has some sort of "large" drive support you can enable.
If you're not booting off the hard drive then I think there were drivers for MS-DOS that performed CHS translation. According an old Microsoft KB article (KB126855) I found "SpeedStor from Storage Dimensions, EZ-Drive from Micro House, and Disk Manager from OnTrack Computer Systems" are possibilities. An IDE controller won't work unless it has its own boot ROM, one that can perform CHS translation.