Now there's a can of worms.
Indeed, I picked these FPGA accelerators for the amiga because they are (were? I don't know what the state is) absolutely ridiculous. The problem with the Amiga in particular is that the chipset will always run at it's slow ~7 Mhz. The entire system is built around that clock (really build around the PAL/NTSC color clock frequencies, these are divisons) and you can't change anything here without changing *everything*, so screen refresh rate, audio sampling rate and disk drive speed, which as you can imagine, would not end well. It's set in stone. (There would've been the possibility to run parts of the system actually "asynchronously" but they didn't because basically the fast, additional memory required was very, very expensive but that's neither here nor there) I have a 68060 50 Mhz accelerator card for my Amiga 2000. The 68060 is an uncommon processor (to most end users, it was in a lot of stuff though, from airplanes to missiles to telco to space shuttles to BMWs) but to make it more relatable, it's about the speed of an early pentium. There are not many of these cards because implementing this on an accelerator was not that easy in the early 90s for a small outfit and it was also kinda pointless because the PC already reigned supreme so you were restricted to a market of people romantically attached to their Amiga in the 90s of which there were suprisingly many but not that many. Main use for such cards was to run 68k Mac "emulation" (not really emulation, it's more like linux' WINE really) to have a bigger software library which the Amiga can pull off flawlessly, making an 68060 equipped Amiga the fastest 68k Mac platform you can have, on "authentic, time-appropiate" hardware. This got somewhat forgotten but these 68k Macs were expensive and an accelerator for the Amiga gave you both the capability to run your old AmigaOS software and newer Mac stuff, which is one thing that made them attractive for a few years. An 68060-equipped Amiga 2000 is fast enough to run Mac games like Capitalism, Day of the Tentacle, Full Throttle and Star Trek TNG: A final Unity, which is quite the gamut for a system from 1987.
The 2000 is strictly 16 bit memory bus and very slow so the 68060 has local 32 bit memory on the card. (otherwise it'd be utterly pointless and the processor would just wait on the slow system ram all the time) This is ok for CPU bound tasks and actually really quick, especially when you use the accelerator-local SCSI controller with DMA so you have to pipe as little data through the slow Amiga part as possible. Sadly, the 68060 has to talk to the rest of the system sometimes, especially in chipset-bound operations involving sound, graphics etc.. The "timing window" for the 68060 on this particular accelerator to talk to the chipset is actually so unfavorable that chipset-bound operations are SLOWER than on an unaccelerated Amiga. Videogames played via e.g. whdload in some cases run actually slower than just directly booted from a floppy with the accelerator turned off, not because the individual parts are slower, but because there's so much delay in them being able to talk to each other.
One solution you can implement to avoid that slow chipset further (while still being bound to the just as slow Zorro II, so really not that much of an improvement) is adding a graphics card to the system and then get clever with memory access times, caching and so on. There weren't really graphics chips made for the Zorro bus (because it was such a tiny marketshare it would have not been profitable) so all "classic" graphics cards that exist for the Amiga have graphics chips that were either made for the ISA or the PCI bus. The amiga graphics cards then have glue logic so they speak PCI/ISA to the chip and Zorro to the system. This was quite timing critical too and even though we had programmable logic it was finnicky, not that trivial to implement in the early 90s. On top of that the OS never really supported this. Promises by Commodore were made and not kept and you know the rest. Then there were 3rd party libraries to patch this into the OS but they had some gay licensing slapfights going on and I don't even remember the story there I think it's actually still going on because autism. There are also accelerators that completely bypass the Zorro system an have a local bus from the accelerator to a graphics card which is of course the fastest you can go. I have a graphics card for that Amiga. It's kinda useless on the "amiga side" of things, but again, great for 68k Mac emulation since MacOS software goes cleanly through the OS and isn't just a bunch of chipset-poking hacks.
Why am I telling you all this? We're now in the world of tomorrow and both the 68060 and the amiga chipsets are trivial, downright primitive and easy to implement in an FPGA. And that's what the FPGA accelerator people did, they just implemented the entire computer in the FPGA and avoided all these complicated speed bumps and timing problems. With these FPGAs, the Amiga is nothing more than an appendix, just forwarding keyboard and other port signals. You might as well remove the Amiga from the equation altogether. This is not putting new wheels on a classic Bentley, this is welding parts of one to your 2013 Honda Civic. At that point you might as well save yourself the money, use the old amiga for old amiga things and run an emulator on a more modern machine for those two programs that need something your old Amiga cannot do.
Same, in my opinion, with all these solutions that give you modern outputs (HDMI etc.) for old systems. I don't know what's the newest there but I can promise you they all probably work by just reproducing what the original graphics chip did and then piping it to an digital output. Because it's a lot more trivial to do than processing (often not really good) analog video signals, which is a science in itself. (read: more expensive) There's been made some good progress here in the last few years with the OSSC and Framemeister and what-have-you and I personally just wouldn't, especially since analog video signals was what an Amiga was all about, it's "soul" so to speak.
I think a different case can be made for modern storage solutions. In my "retro religious" beliefs I see a closed microcontroller who e.g. handles SCSI or floppy disk emulation less critical because it's a system that interfaces with the retro computer without replacing any of it's parts. The old SCSI drives, disk drives etc. weren't any different, they had their own onboard microcontrollers too, even if a lot more primitive. If you put a "modern" SCSI server drive (one of the few drives you can still get that still work well- which is possible, SCSI is backwards compatible) into an old Amiga for example, you end up with a drive whose microcontroller probably has many times the RAM and processing power the entire system has, so it isn't really any different, just more inconvinient.
I'd write more about how you can easily build 8 and 16 bit systems time appropiate with cheap off the shelf parts, but this post is long enough.