DosBox with 68k Dynamic Recompilation should be able to achieve 386 emulation speeds on a fast 68060 or fpga 68k CPU. The bonus is that the Amiga can multitask at the same time
Problem is that some of the interesting applications and reason to run 80386 software on real hardware is very low latency. This is very true for parallelport bitbanging DOS software. So it's the same issue as with software emulated Amigas. They can't deal with latency and propagation races properly.
So a very common setup like 80386+VGA+Soundblaster with many lovely parallelports would be just the thing to make use of existing DOS bitbanging software.
@MikeJ, If you succeed to run TurboC in 80286 mode using outportb(0x378,0xF0) etc and some VGA demos with sound I thing the re-implementation can be called a success.
A more specific setup would be:
CPU: 80386 - least complex x86-processor with the greatest software compatibility
FPU: 80387 - IF space is available
Video: VGA -perhaps CGA/EGA as options, again for compatibility
Sound: Soundblaster 16
HDD: P-ATA < 8GB
Floppy: 2x 1,44MB
Serial: 16550 that can dump contents to flash or use Ethernet
Parallel: 8255 with real world I/O
Ethernet: NE2000
Of course OSD options to enable/disable as desired could be used. And loadable setups associated with a bootimage etc.
The main point is 80386+VGA and access to I/O via (many) parallelports such that bitbanging DOS stuff can be made to work. So rather more real world I/O than anything else. By using 80386 instead of 8086/286 one get the benefit of being able to run Unix or Windows. Perhaps one could fix the ten or so 80386 errata (bugs) at the same time.