There is no known reason why the Deneb should be run in Zorro II mode in Zorro III capable machines. Zorro III PIO should always work in A3000/A4000D/A4000T. Zorro III DMA should also work in A3000 with no other DMA masters.
If you're using a Buster Rev. 9, you should install the DenebBuster9IDTag in flashrom and/or set the enviroment variable to reflect this (there is a readme about this in the Poseidon and Luciferin archives). As far as I know, this only is necessary for DMA mode on Buster 9 machines.
Some CPU board incorrectly set the Zorro III space to cachable at init even before the Poseidon kicks in and this can cause the hardware driver to fail to open (this does not seem to be the case here though). However, it might be still wise to check the MMU setup of the Zorro III region (because Zorro II is always cache-inhibit, but Zorro III might not be) especially on 68040/68060 machines. You might want to try out Thomas Richter's MMU library.
The DMA engine of the Deneb is only activated on larger transfers, so mice and keyboards will not trigger it -- you will need an USB stick to test it.
It always helps to have the latest firmware version, which can be obtained at
http://www.e3b.de -- there were some specific fixes I cannot remember though. Michael will know (if you send him an email today, it's his birthday).
In Zorro III mode, the denebz2usb.device will fail to open. In Zorro II mode, both denebdmausb.device and denebpiousb.device will fail to open. So you need to select the right device in trident for your system configuration.
I know at least one user who is using the Deneb in Zorro III mode in his machine without problems.
Other than the Buster9IDTag and the wrong cache settings, Zorro II/III has no relevance to flashrom whatsoever (except that the Zorro II space is limited and putting the card in Zorro II mode will take up 128 KB address space instead of 64 KB).
Be aware that some software system hacks in the past have caused trouble of all sorts. To be sure that your system is clean, boot without startup-sequence with Poseidon in flashrom (use the quick setup menu item). Mount the stick, check if you can access it. If this doesn't work, try running setpatch before and after mounting the usb stick.
Also, other Zorro III board have known to interfere because of them violating the Zorro III timings and specs (Picasso IV). For the latter, all known problems have been fixed.
The latest version of Poseidon is V4.4.