You're lucky you can find printers that can use font suitcases, that's cool.
Reading the rest of your latest post, I see what you mean now. You're referring to old Mac suitcase style fonts, like from OS 9 or earlier. MS Office (even the 2011 version) installs them. Most printers now do prefer you not send those. Or as you found, they won't take them at all.
Thanks for the links, I tried Font2Web, but it says "This file type is not supported. You can only upload .ttf and .otf files"
There would be at least two reasons for that. One, legacy Mac TrueType suitcase fonts have no font data in the data fork (nor do Mac Type 1 PostScript). Everything is in the resource fork. So as far as such sites are concerned, they see the font as empty.
The other is that such fonts, and .ttc fonts, contain or can contain multiple type faces. Up to 999 of them. So the site either doesn't know what to do with them, or they just won't attempt to figure out if you mean you want all of them converted, or only some.
.otf or .ttc fonts work because the data is in the data fork, and they will be only one typeface, so such site's have no confusion as to how to handle them.
What you can do in the meantime is purchase the pro version of TransType 3. Though I'd first check to see if you get a free upgrade to version 4 when it's ready. With version 3, you can first convert all of your suitcase fonts into individual OpenType fonts, then feed them to the web sites I linked to covert the .otf fonts to webfonts. Roundabout, but it would work.