Is there a way to get a larger HD with the IDE in an amiga 4000?
Yes.
You need filesystem capable of 64bit access (standard 3.1 FFS won't do, but
ffstd64 might help. SFS or PFS3 are nice). You also need to patch the scsi.device to handle 64bit access. It can be done with scsi43, amigaos 3.5/3.9 or
idefix for example. When formatting >4GB are partition with OS 3.1 format you must always use "quick format". OS 3.1 HDToolBox will also display funny values when it identifies a large HDD, so you might want to use a replacement partitioning tool.
In any case,
check4gb is useful when hacking things up.
Final note: Various OS 3.1 components don't handle huge partition size correctly: c:format, c:info, installer and Workbench are affected at least. These problems are mostly not fatal however, just annoying (wrong free storage displayed, installer complaining disk is full when it obviously isn't). The only potentially fatal component is the disk format operation. You must always remember to use the "quickformat" option.
"Hard Drive Controller: IDE (2Gb maximum capacity)"
That's incorrect. The controller doesn't have any limit, the driver does. The stock OS 3.1 device driver is limited to 4GB. IDEFix/OS3.5/3.9 driver have limit of 137GB (128GiB).