Firstly, Adobe Illustrator native files are not technically supported by Ghostscript at all. They might work, because they are normally either PostScript or PDF files with custom bits that can be ignored for the purposes of drawing the content. But its not a guarantee.
Secondly; no, do not multiply convert the files! That's a piece of cargo cult mythology that's been doing the rounds for ages. There are sometimes reasons for doing so bu in general this will simply magnify problems, not solve them. Really, don't do that.
You haven't quoted the errors you are getting and you haven't supplied any files to look at, so its not really possible to tell what your problem is. I have no clue what an 'artboard' is, and a picture of the Illustrator dialog doesn't help I'm sorry to say.
Perhaps if you could supply an example file, and maybe a picture of what you expect, it might be possible to figure it out. My guess is that your '.ai' file is a PDF file, and that it has a MediaBox (which is what Ghostscript uses by default) and an ArtBox which is what you actually want to use. Or something like that. Hard to say wihtout more information.
[EDIT]
Well, I'm afraid the answer here is that you can't easily get what you want from that file without using Illustrator.
The file is a PDF file (if you rename input.ai to input.pdf then you can open it with a PDF reader). But Illustrator doesn't use most of the PDF file when it opens it. Instead the PDF file contains a '/PieceInfo' key, which is a key in the Page dictionary. That points to a dictionary which has a /Private key, which (finally!) points to a dictionary with a bunch of Illustrator stuff:
52 0 obj
<<
/AIMetaData 53 0 R
/AIPrivateData1 54 0 R
/AIPrivateData10 55 0 R
/AIPrivateData11 56 0 R
/AIPrivateData2 57 0 R
/AIPrivateData3 58 0 R
/AIPrivateData4 59 0 R
/AIPrivateData5 60 0 R
/AIPrivateData6 61 0 R
/AIPrivateData7 62 0 R
/AIPrivateData8 63 0 R
/AIPrivateData9 64 0 R
/ContainerVersion 11
/CreatorVersion 23
/NumBlock 11
/RoundtripStreamType 1
/RoundtripVersion 17
>>
endobj
That's the actual saved file format of the Illustrator file. You can think of the PDf file as a 'preview' wrapped around the Illustrator native file. Illustrator reads the PDF file to find its own data, then throws the PDF file away and uses the native file format stored within it instead.
The problem is that the PDF part of the file simply doesn't contain the content you want to see. That's stored in the Illustrator native data. Ghostscript just renders what's in the PDF file, it doesn't look at the Illustrator native file.
Looking at the Illustrator private data, some of it is uncompressed, but most is compressed, it doesn't say how it is compressed but applying the FlateDecode filter produces a good old-fashioned Illustrator PostScript file, one that will work with Ghostscript.
But you would have to manually parse the PDF file, extract all the compressed AIPrivateData streams, concatenate them together, apply the FlateDecode filter to decompress them, and only then send the resulting output to Ghostscript with the -dEPSCrop switch set. That will result in the output you want.
But neither Ghostscript nor ImageMagick (which generally uses Ghostscript to render PDF files) will do any of that for you, you would have to do it all yourself.
