Hi again,
I'm curious how the original poster has decided on 3:1 as what they need. Are you trying to photograph something that's a known size? 3:1 on a 1.6X crop sensor camera would be a subject about 7.5mm by 5mm. Or, 3:1 on a full frame sensor or 35mm film camera would be a subject about 12 x 8mm. Are you really shooting that small objects frequently? Any way a 2:1 image could simply be cropped a bit?
The higher your magnification and the longer your lens focal length, the shallower your DOF will be. It begins to get razor thin above 2:1. You'll either need to work with that or stop down your primary lens a lot to get back some of the DOF, slowing the shutter speed and/or upping the ISO to compensate, and possibly using a flash as well.
Any lens weaknesses will be greatly magnified right along with the subject matter. That's another reason zooms aren' t usually very useful for reversing (in addition to the smaller max aperture of the reversed lens and resulting dimmer viewfinder you'll need to deal with).
I looked up the Sigma 105mm and see that it uses a 58mm filter. That being the case, your safest bet for a lens to reverse on the front of it would be the Canon 50/1.4, which also uses a 58mm filter. Actually you might use any other 50 that uses a 58mm filter or larger, but I can't think of many that do. You may be able get by with a 50 that uses a 55mm filter, which is more common: older Konica and Minolta MF lenses come to mind as a couple brands that used that filter size a lot, including 50/1.7 and 50/1.4 Hexanons and Rokkors. Earlier Canon FD 50s had a 55mm thread too, but with them you need a special "reversing" device that doubles as a lens hood on the back of the lens, to maintain wide open aperture when FD lenses are not mounted normally on a camera. Perhaps some earlier Nikkors used 55mm or 58mm, but I'm more familiar with the AI/AI-S all of which use 52mm filters and leave you no better off than a Canon 50/18. Same is true of the later Canon FD "New" lenses, they used 52mm filters and still have the same issue of the aperture that partially closes when unmounted. Pentax and others tended to use 49mm filters size on most of their 50s that I know of.
But, it's always a bit of "luck of the draw" that any particular reversed lens will play well together with your primary lens.
The teleconverter example shown is better than I'd have expected.
I'd still be inclined to try extension tubes instead.
If the 68mm of extension from a set of Kenko tubes (which includes a 36mm, 20mm and 12mm, for approx. $160 a set) gets to 2:1, then to get to 3:1 I'm estimating you'd need a bit over 100mm of total extension.
In that case, you could instead get two sets of Adorama's Pro Optic tubes (which include 31mm, 21mm and 13mm, for approx. $85 per set) and use two of the 31mm and two of the 21mm, for a total of 104mm.
Some day I'm going to cobble together a macro bellows for use with EOS. I suspect I could make one work by using short extension tubes in EF mount on the front and back and soldering wires to the contacts to allow them and the lens and camera to communicate with one another. However, I'll leave that little project for a more ambitious day! (Or I'll just buy the Novoflex that offers this.)
The camera's built in flash is pretty much worthless for macro shooting (and... IMO... most other things). There are specialized macro flashes, mostly two types: ring lights and twin lights. Both can be mounted on the front of a lens (however a Canon flash probably won't bayonet onto a Sigma lens... more on how to get around that in some cases a moment.)
Personally, I'm not a big fan of ring lights for macro. I just feel they give too flat lighting for my uses. That's perfect if you are photographing stamps and coins or medical/dental and similar. However, I mostly use macro for small critters and plants and prefer more shadow play to give a sense of depth to the image.
So, one macro flash I use is Canon's Twinlite. It works well, however I have modified it to work on a Lepp/Stroboframe macro flash bracket instead of using the lens mounting system that Canon provides. The Lepp bracket has two arms that allow a lot more flexibility positioning the two small flash heads. It would also work just fine with any non-Canon lenses, where the Canon lens mount method doesn't work.
However, the Twinlite isn't cheap, and the Lepp bracket adds even more cost. Plus, it's a fairly sizeable rig to lug around and use.
An alternative is to work with a single flash instead. Any of the Canon ETTL flashes will work (220/420/430/550/580EX... 220EX is small, but only highly automated in operation). Just use an off-camera shoe cord and position the flash where you want it by hand or on some sort of simple bracket. I use 550EX this way a lot, when I don't happen to have the Twinlite with me.
Now, you'd think a single flash would cause too deep shadows and a highly contrasty effect. But, with macro it doesn't. The reason is that the flash head is like a giant soft soft box in the sky to tiny subjects. So the light tends to wrap around and fill the shadows very nicely. And, if you happen to want more fill, it's dead simple to use a white card or something similar to bounce a bit more fill into the shadows.
The biggest concern working up close with one of these flashes is that they will over-power the subject. There's are simple work-arounds for this too. One is just to position the flash a little farther away from the subject. Another thing you can do is pick up a roll of white gauze bandage at a pharmacy and snip off a few pieces, than put a layer or two or three over the flash to diffuse and reduce the light output. Secure in place with a rubber band. This works very well and the ETTL system continues to work perfectly. Finally, there are also accessory mini soft boxes you can fit to most accessory flashes. These will also work well.
Just be a little cautious positioning the flash so that it's not directed back into the lens, unless you are going for some sort of special effect.
Recently I've seen some flashes that are "light panels", as well as others that use continuous LEDs. Both these might be useful with macro shooting, but ETTL is nice and something I'd not give up too quickly in the case of the light panel. Continuous light would be better, but might scare away some subjects.