The Mame license states that the INFORMATION in the Mame source about the hardware being emulated is free to use for anyone, for any purpose. Basically, it should be possible to write an emu based on the Mame code, without actually using the Mame source for anything other than reference.
The problem there is that the information contained in the MAME source
is the source. There's really not a lot of difference between reading code and using that to write equivalent code, and using copy/paste to put their code in your project. I think the MAME license is a little self-contradictory in that sense, and I can't really speculate too far on what they intend people to do with the information in the source other than use it to emulate machines MAME supports by copying code.
One way to resolve this issue would be to document what information you're harvesting from MAME and minimize it as much as possible. For instance, if you're emulating a game that uses a specific processor, try to find emulation code for that processor from another source, seek specific information about the game from MAME.
IMO, as a programmer, if you wrote such a thing using MAME as one of your primary sources of information, you would have some obligations. The first one would be to acknowledge MAME in your documentation. The alternative, IMO, is plagiarism. (Of course, you started on this because you wanted to avoid using "MAME", so having to acknowledge them might not help you much...) The second obligation would be to follow the terms of the MAME license with regard to donating code back to MAME (at least anything relevant to emulating the machines - I'd say framework for pretty-fying the application, interfacing with the OS, etc. needn't be donated back, so long as you don't read their code for that...)
When exactly did MAME switch away from GPL? If the old versions used to be GPL, then they still are. If there's a GPL-version that supports the games you want, then you could adapt the code to make your own GPL-licensed variant. Of course, even if you can take code from an old GPL version of MAME that does what you need, that still doesn't release you from the obligation to acknowledge the original authors IMO.
If you really want to know what's legit and what's not, contact the MAME team. But I suspect they won't have the answer you want.