According to the technical specs Apple published in a Developer note on the Classic, with 440 mah you are clearly overloading the 12 volts rail.

Inrush current to spin-up the drive will be even higher, probably more than 1A, so the hard drive you have isn't probably going to work or not for long anyway...

Here's the paper with all the technical specs. On page 19 in Table 1-3, you can see the power limitations for the hard drive.

http://developer.apple.com/legacy/mac/library/documentation/Hardware/Developer_Notes/Macintosh_CPUs-68K_Desktop/Mac_Classic.pdf

If you want a large HDD that draws less power, go for a 5400 rpm at most.

Another option, since you already have a SCSI to IDE adapter, is to use this combined with a 2.5" SSD IDE drive.

I have an SE/30 with an SSD drive combined with an Acard SCSi-IDE adapter and it works great, using very little power too.